Applying and analysing trigonometric functions

It is given that cos = k, where k is a constant and 0 < x < 90. Find in terms of k for sin 2x

• 2k $\sqrt{1-k^2}$ 

• -2k  $\sqrt{1-k^2}$  

• 2k

•  $\sqrt{k^2-1}$  

 $45\degree$  

•  $\frac{\pi}{4}$  

•  $\frac{11\pi}{72}$  

•  $\frac{23\pi}{120}$  

•  $\frac{\pi}{6}$  

 $\tan\left(90\ +\theta\right)=$  

•  $-\cot\theta$  

•  $\cot\theta$  

•  $\tan\ \theta$  

•  $-\tan\ \theta$  

csc(90⁰-θ) = 

• secθ
• sinθ
• cosθ
• tanθ

• A

• B

• C

• D

 $\sqrt{2+\sqrt{2+2\cos4x}}=$  

•  $2\cos\ x$  

•  $2\sin\ x$  

•  $2\ \cos2x$  

•  $\cos\ x$  

If f(x) = sin³(2x), then f'(x) =

• 3cos(2x)
• 3sin(2x)⋅2
• 3sin²(2x)cos(2x)
• 3sin²(2x)cos(2x)⋅2

 $\cos129\degree+\cos45\degree$  

•  $-2\cos87\degree\cos42\degree$  

•  $-2\sin87\degree\sin42\degree$  

•  $-2\sin87\degree\cos42\degree$  

•  $2\cos87\degree\cos42\degree$  

Given that cos P=   $-\frac{4}{5}$  and cos Q =  $\frac{12}{13}$   such that P and Q are angles in third and fourth quadrant respectively. Find the values of sin (P + Q) .       

•  $-\frac{56}{65}$  

•  $\frac{56}{65}$  

•  $\frac{16}{65}$  

•  $-\frac{16}{65}$