Hyperbolic Trig Identities

What is the hyperbolic identity for the trig identity:

 $\sin^2x+\cos^2x=1$  ?

•  $-\sinh^2x-\cosh^2x=1$  

•  $\sinh^2x+\cosh^2x=1$  

•  $\cosh^2x-\sinh^2x=1$  

•  $\cosh^2x-1=\sinh^2x$  

State the hyperbolic trig identity for the trig identity:

 $\tan x=\frac{\sin x}{\cos x}$  

•  $\tanh x=\frac{\sinh x}{\cosh x}$  

•  $-\tanh x=\frac{\sinh x}{\cosh x}$  

•  $\tanh x=\frac{-\sinh x}{\cosh x}$  

•  $-\tanh x=\frac{-\sinh x}{\cosh x}$  

State the hyperbolic trig function for the trig function:

 $\sec x-\cos x=\sin x\tan x$  

•  $\operatorname{sech}x-\cosh x=\sinh x\ \tanh x$  

•  $\cosh x-\operatorname{sech}x=\sinh x\tanh x$  

•  $\cosh x+\operatorname{sech}x=\sinh x\tanh x$  

•  $\operatorname{sech}x-\cosh x=-\sinh x\tanh x$  

State the hyperbolic trig function for:

 $\cos2x=2\cos^2x-1$  

•  $\cosh\left(2x\right)=2\cos^2\left(x\right)-1$  

•  $\cosh\left(2x\right)=2\cosh^2x-1$  

•  $\cosh\left(2x\right)+1=2\cosh^2x$  

•  $\cosh\left(2x\right)-2\cosh^2x=1$  

What is the hyperbolic trig identity corresponding to:

 $\sin^2\left(\frac{x}{2}\right)=\frac{1}{2}\left(1-\cos\left(x\right)\right)$  

•  $\sinh^2\left(\frac{x}{2}\right)=\frac{1}{2}\left(1-\cosh\left(x\right)\right)$  

•  $\sinh^2\left(\frac{x}{2}\right)=\frac{1}{2}\left(\cosh\left(x\right)-1\right)$  

•  $\sinh^2\left(\frac{x}{2}\right)=\frac{1}{2}\left(1+\cosh\left(x\right)\right)$  

•  $\sinh^2\left(\frac{x}{2}\right)=\frac{1}{2}\left(1-\cos\left(x\right)\right)$  

What is the hyperbolic trig identity for:

 $\operatorname{cosec}^4x-\cot^4x=\operatorname{cosec}^2x+\cot^2x$  

•  $\operatorname{cosech}^4x+\coth^4x=\operatorname{cosech}^2x+\coth^2x$  

•  $\operatorname{cosech}^4x-\coth^4x=\operatorname{cosech}^2x+\coth^2x$  

•  $\operatorname{cosech}^4x-\coth^4x=-\operatorname{cosech}^2x-\coth^2x$  

•  $\operatorname{cosech}^4x-\coth^4x=\operatorname{sech}^2x-\coth^2x$  

State the hyperbolic trig equation for:

 $\sin\left(3\theta\right)=3\sin\left(\theta\right)-4\sin^3\left(\theta\right)$  

•  $\sinh\left(3\theta\right)=3\sinh\left(\theta\right)-4\sinh^3\left(\theta\right)$  

•  $\sinh\left(3\theta\right)=4\sinh^3\left(\theta\right)-3\sinh\left(\theta\right)$  

•  $\sinh\left(3\theta\right)=-4\sinh^3\left(\theta\right)-3\sinh\left(\theta\right)$  

•  $\sinh\left(3\theta\right)=3\sinh\left(\theta\right)+4\sinh^3\left(\theta\right)$  

State the hyperbolic trig identity for:

 $\cos\left(A+B\right)$  

•  $\cosh\left(A\right)\cosh\left(B\right)-\sinh\left(A\right)\sinh\left(B\right)$  

•  $\cosh\left(A\right)\sinh\left(B\right)+\cosh\left(B\right)\sinh\left(A\right)$  

•  $\cosh\left(A\right)\cosh\left(B\right)+\sinh\left(A\right)\sinh\left(B\right)$  

•  $\sinh\left(A\right)\sinh\left(B\right)-\cosh\left(A\right)\cosh\left(B\right)$  

What is the hyperbolic trig identify for
 $\tan\left(A-B\right)$  ?

•  $\frac{\tanh\left(A\right)-\tanh\left(B\right)}{1+\tanh\left(A\right)\tanh\left(B\right)}$  

•  $\frac{\tanh\left(A\right)+\tanh\left(B\right)}{1-\tanh\left(A\right)\tanh\left(B\right)}$  

•  $\frac{\tanh\left(A\right)-\tanh\left(B\right)}{1-\tanh\left(A\right)\tanh\left(B\right)}$  

•  $\frac{\tanh\left(A\right)+\tanh\left(B\right)}{1+\tanh\left(A\right)\tanh\left(B\right)}$  

State the hyperbolic identity for the trig identity:

 $4\operatorname{cosec}^2\left(2x\right)-\operatorname{cosec}^2\left(x\right)=\sec^2\left(x\right)$  

•  $4\operatorname{cosech}^2\left(2x\right)-\operatorname{cosech}^2\left(x\right)=\operatorname{sech}^2\left(x\right)$  

•  $\operatorname{cosech}^2\left(x\right)-4\operatorname{cosech}^2\left(2x\right)=\operatorname{sech}^2\left(x\right)$  

•  $4\operatorname{cosech}^2\left(2x\right)+\operatorname{cosech}^2\left(x\right)=\operatorname{sech}^2\left(x\right)$  

•  $4\operatorname{cosech}^2\left(2x\right)-\operatorname{cosech}^2\left(x\right)=-\operatorname{sech}^2\left(x\right)$