Trig Identities: Pythagorean, Sum/Diff, Double, Half-Angle

sin(x) =

• $\frac{1}{\cos\ x}$

• $\frac{1}{\csc\ x}$

• $\frac{1}{\sec\ x}$

• $\csc\ x$

 $1-\cos^2x\$  

•  $\tan^2x$  

•  $\cos\ 2x$  

•  $\sin^2x$  

•  $\sin\ 2x$  

 $\sin\left(x-\frac{3\pi}{2}\right)\ =\$  

• cos x

• sin x

• sin 2x

• sinx cosx

 $\cos\left(x+\pi\right)=\$  

• sin x
  

• cos x

• -sin x

• -cos x

Which of the follow is NOT a way to simplify the following: $\tan^2x\ -\tan^2x\csc^2x$  

•  $\tan^2x\left(1-\csc^22x\right)$  

•  $\frac{\sin^2x}{\cos^2x}-\ \frac{\sin^2x}{\cos^2x}\cdot\frac{1}{\sin^2x}$  

•  $\left(\tan x-\csc x\right)\cdot\left(\tan x+\csc x\right)$  

•  $\tan^2x\left(\cot^2x\right)$  

Which of the following is NOT equivalent to $\frac{2\cos^2x}{\tan^2x}$  

•  $\left(2-2\sin^2x\right)\left(\frac{1}{\cot^2x}\right)$  

•  $\left(2\cos^2x\right)\left(\frac{\sin^2x}{\cos^2x}\right)$  

•  $\sin^22x\left(\cot^2x\right)$  

•  $\frac{2\cos^2x}{\sec^2x-1}$  

Which of the following is Not equivalent to: $2\cos^2x-1$  

•  $\sin^2x$  

•  $2\cos^2x-\left(\sin^2x+\cos^2x\right)$  

•  $\cos^2x-\sin^2x$  

•  $\sin^22x$  

Given:

 $\sin\ x=\frac{-3}{5}\ and\ \pi<x<\frac{3\pi}{2},$  find cos (2x).

•  $\frac{12}{25}$  

•  $-\frac{7}{25}$  

•  $\frac{7}{25}$  

•  $\frac{3\sqrt{10}}{10}$  

Simplfy

 $\sin\left(70\right)\cos\left(20\right)+\cos\left(70\right)\sin\left(20\right)$  

• cos (90)

• sin (90)

• cos(50)

• sin (50)

Simplify: cos(40)cos(50) - sin(40)sin(50).

• sin (10)

• cos (10)

• sin (90)

• cos (90)