cos ⁡ 7 0 o cos ⁡ 4 0 o − sin ⁡ 7 0 o sin ⁡ 4 0 o \cos70^o\cos40^o-\sin70^o\sin40^o\ cos 7 0 o cos 4 0 o − sin 7 0 o sin 4 0 o is equivalent to

cos ⁡ 11 0 o \cos110^o cos 1 1 0 o

cos ⁡ 3 0 o \cos30^o cos 3 0 o

cos ⁡ 7 0 o \cos70^{o\ } cos 7 0 o

sin ⁡ 7 0 o \sin70^{o\ } sin 7 0 o

If sin ⁡ A = 3 5 , sin ⁡ B = 2 3 , \sin A=\frac{3}{5},\sin B=\frac{2}{3}, sin A = 5 3 , sin B = 3 2 , a n d ∠ A a n d ∠ B and\ \angle A\ and\ \angle B a n d ∠ A a n d ∠ B are acute angles, what is the value of cos ⁡ ( A − B ) ? \cos\left(A-B\right)? cos ( A − B ) ?

4 5 + 6 15 \frac{4\sqrt{5}+6}{15} 1 5 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 6

4 5 − 6 15 \frac{4\sqrt{5}-6}{15} 1 5 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 6

4 5 + 2 5 \frac{4\sqrt{5}+2}{5} 5 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 2

If cos ⁡ A = 1 3 \cos A=\frac{1}{3} cos A = 3 1 , then the positive value of tan ⁡ A 2 \tan\ \frac{A}{2} tan 2 A ?

2 2 \frac{\sqrt{2}}{2} 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

3 \sqrt{3} 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

3 3 \frac{\sqrt{3}}{3} 3 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

If sin ⁡ A = 4 5 , tan ⁡ B = 5 12 , \sin A=\frac{4}{5},\tan B=\frac{5}{12}, sin A = 5 4 , tan B = 1 2 5 , and A and B are first quadrant angles, what is the value of sin ⁡ ( A + B ) \sin\left(A+B\right) sin ( A + B ) ?

− 33 65 -\frac{33}{65} − 6 5 3 3

− 63 65 -\frac{63}{65} − 6 5 6 3

sin ⁡ 9 6 o cos ⁡ 2 4 o + cos ⁡ 9 6 o sin ⁡ 2 4 o \sin96^o\cos24^o+\cos96^o\sin24^o\ sin 9 6 o cos 2 4 o + cos 9 6 o sin 2 4 o is equivalent to

sin ⁡ 12 0 o \sin120^o sin 1 2 0 o

sin ⁡ 7 2 o \sin72^{o\ } sin 7 2 o

cos ⁡ 12 0 o \cos120^o cos 1 2 0 o

cos ⁡ 7 2 o \cos72^o cos 7 2 o

The expression 2 sin ⁡ 3 0 o cos ⁡ 3 0 o 2\sin30^o\cos30^o 2 sin 3 0 o cos 3 0 o has the same value as

sin ⁡ 6 0 o \sin60^o sin 6 0 o

sin ⁡ 1 5 o \sin15^o sin 1 5 o

cos ⁡ 6 0 o \cos60^o cos 6 0 o

cos ⁡ 1 5 o \cos15^o cos 1 5 o

If x is a positive acute angle and sin ⁡ x = 1 2 , \sin x=\frac{1}{2}, sin x = 2 1 , what is sin ⁡ 2 x ? \sin2x? sin 2 x ?

3 2 \frac{\sqrt{3}}{2} 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 3 2 -\frac{\sqrt{3}}{2} − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

If cos ⁡ θ = 1 8 , \cos\theta=\frac{1}{8}, cos θ = 8 1 , the positive value of sin ⁡ θ 2 \sin\ \frac{\theta}{2} sin 2 θ is

7 4 \frac{\sqrt{7}}{4} 4 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Sum Difference Double Half Angles Identities

Authored by Hung Tran

Mathematics

11th - 12th Grade

CCSS covered

Used 472+ times

Sum Difference Double Half Angles Identities

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10 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$\cos70^o\cos40^o-\sin70^o\sin40^o\$ is equivalent to

$\cos30^o$

$\cos70^{o\ }$

$\cos110^o$

$\sin70^{o\ }$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are acute angles, what is the value of $\cos\left(A-B\right)?$

$-\frac{2}{3}$

$\frac{4\sqrt{5}-6}{15}$

$\frac{4\sqrt{5}+2}{5}$

$\frac{4\sqrt{5}+6}{15}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If $\cos A=\frac{1}{3}$ , then the positive value of $\tan\ \frac{A}{2}$ ?

$\sqrt{2}$

$\sqrt{3}$

$\frac{\sqrt{3}}{3}$

$\frac{\sqrt{2}}{2}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If $\tan A=\frac{2}{3}\ and\ \tan B=\frac{1}{2},$ what is the value of $\tan\left(A+B\right)?$

$\frac{1}{8}$

$\frac{7}{8}$

$\frac{1}{4}$

$\frac{7}{4}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If $\sin A=\frac{4}{5},\tan B=\frac{5}{12},$ and A and B are first quadrant angles, what is the value of $\sin\left(A+B\right)$ ?

$\frac{63}{65}$

$-\frac{33}{65}$

$\frac{33}{65}$

$-\frac{63}{65}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$\sin96^o\cos24^o+\cos96^o\sin24^o\$ is equivalent to

$\sin120^o$

$\sin72^{o\ }$

$\cos120^o$

$\cos72^o$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The expression $2\sin30^o\cos30^o$ has the same value as

$\sin15^o$

$\cos60^o$

$\sin60^o$

$\cos15^o$

Tags

CCSS.HSG.SRT.C.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If x is a positive acute angle and $\sin x=\frac{1}{2},$ what is $\sin2x?$

$-\frac{1}{2}$

$\frac{1}{2}$

$-\frac{\sqrt{3}}{2}$

$\frac{\sqrt{3}}{2}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If $\cos\theta=\frac{1}{8},$ the positive value of $\sin\ \frac{\theta}{2}$ is

$\frac{3}{2}$

$\frac{\sqrt{7}}{4}$

$\frac{9}{16}$

$\frac{3}{4}$

Tags

CCSS.HSF.TF.C.9

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If $\sin\theta=\frac{\sqrt{5}}{3}$ , then $\cos2\theta$ equals

$\frac{1}{3}$

$-\frac{1}{3}$

$\frac{1}{9}$

$-\frac{1}{9}$

Tags

CCSS.HSF.TF.C.9

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Sum Difference Double Half Angles Identities

cos⁡70ocos⁡40o−sin⁡70osin⁡40o \cos70^o\cos40^o-\sin70^o\sin40^o\ cos70ocos40o−sin70osin40o is equivalent to

If sin⁡A=35,sin⁡B=23,\sin A=\frac{3}{5},\sin B=\frac{2}{3},sinA=53​,sinB=32​, and ∠A and ∠Band\ \angle A\ and\ \angle Band ∠A and ∠B are acute angles, what is the value of cos⁡(A−B)?\cos\left(A-B\right)?cos(A−B)?

If cos⁡A=13\cos A=\frac{1}{3}cosA=31​ , then the positive value of tan⁡ A2\tan\ \frac{A}{2}tan 2A​ ?

If tan⁡A=23 and tan⁡B=12,\tan A=\frac{2}{3}\ and\ \tan B=\frac{1}{2},tanA=32​ and tanB=21​, what is the value of tan⁡(A+B)?\tan\left(A+B\right)?tan(A+B)?

If sin⁡A=45,tan⁡B=512,\sin A=\frac{4}{5},\tan B=\frac{5}{12},sinA=54​,tanB=125​, and A and B are first quadrant angles, what is the value of sin⁡(A+B)\sin\left(A+B\right)sin(A+B) ?

sin⁡96ocos⁡24o+cos⁡96osin⁡24o \sin96^o\cos24^o+\cos96^o\sin24^o\ sin96ocos24o+cos96osin24o is equivalent to

The expression 2sin⁡30ocos⁡30o2\sin30^o\cos30^o2sin30ocos30o has the same value as

If x is a positive acute angle and sin⁡x=12,\sin x=\frac{1}{2},sinx=21​, what is sin⁡2x?\sin2x?sin2x?

If cos⁡θ=18,\cos\theta=\frac{1}{8},cosθ=81​, the positive value of sin⁡ θ2\sin\ \frac{\theta}{2}sin 2θ​ is

If sin⁡θ=53\sin\theta=\frac{\sqrt{5}}{3}sinθ=35​​ , then cos⁡2θ\cos2\thetacos2θ equals

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$\cos70^o\cos40^o-\sin70^o\sin40^o\$ is equivalent to

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are acute angles, what is the value of $\cos\left(A-B\right)?$

If $\cos A=\frac{1}{3}$ , then the positive value of $\tan\ \frac{A}{2}$ ?

If $\tan A=\frac{2}{3}\ and\ \tan B=\frac{1}{2},$ what is the value of $\tan\left(A+B\right)?$

If $\sin A=\frac{4}{5},\tan B=\frac{5}{12},$ and A and B are first quadrant angles, what is the value of $\sin\left(A+B\right)$ ?

$\sin96^o\cos24^o+\cos96^o\sin24^o\$ is equivalent to

The expression $2\sin30^o\cos30^o$ has the same value as

If x is a positive acute angle and $\sin x=\frac{1}{2},$ what is $\sin2x?$

If $\cos\theta=\frac{1}{8},$ the positive value of $\sin\ \frac{\theta}{2}$ is

If $\sin\theta=\frac{\sqrt{5}}{3}$ , then $\cos2\theta$ equals