91Ó°ÊÓ

Verify that each equation is an identity. $$\sin ^{2} \frac{x}{2}=\frac{\tan x-\sin x}{2 \tan x}$$

Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures. $$\cot x+\sqrt{3}=0$$

Give the exact real number value of each expression. Do not use a calculator. $$\cos \left(\cos ^{-1} \frac{\sqrt{3}}{2}\right)$$

Verify that each equation is an identity. $$\frac{\cot \alpha-\tan \alpha}{\cot \alpha+\tan \alpha}=\cos 2 \alpha$$

Perform indicated operation and simplify the result. $$\frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{1+\cos \theta}$$

Give the exact real number value of each expression. Do not use a calculator. $$\sin ^{-1}\left(\sin \frac{4 \pi}{3}\right)$$

Perform indicated operation and simplify the result. $$(1+\sin t)^{2}+\cos ^{2} t$$

Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures. $$6 \sin ^{2} \theta+\sin \theta=1$$

Verify that each equation is an identity. $$\cos 2 x=\frac{1-\tan ^{2} x}{1+\tan ^{2} x}$$

Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures. $$3 \sin ^{2} \theta-\sin \theta=2$$