91Ó°ÊÓ

Use an identity to solve each equation on the interval \([0,2 \pi)\) $$ \cos 2 x=\sin x $$

Rewrite each expression as a simplified expression containing one term. $$ \frac{\cos (\alpha-\beta)+\cos (\alpha+\beta)}{-\sin (\alpha-\beta)+\sin (\alpha+\beta)} $$

Use an identity to solve each equation on the interval \([0,2 \pi)\) $$ \cos 2 x+5 \cos x+3=0 $$

Rewrite each expression as a simplified expression containing one term. $$\cos \left(\frac{\pi}{6}+\alpha\right) \cos \left(\frac{\pi}{6}-\alpha\right)-\sin \left(\frac{\pi}{6}+\alpha\right) \sin \left(\frac{\pi}{6}-\alpha\right)$$ (Do not use four different identities to solve this exercise.)

Use an identity to solve each equation on the interval \([0,2 \pi)\) $$ \cos 2 x+\cos x+1=0 $$

Rewrite each expression as a simplified expression containing one term. $$\sin \left(\frac{\pi}{3}-\alpha\right) \cos \left(\frac{\pi}{3}+\alpha\right)+\cos \left(\frac{\pi}{3}-\alpha\right) \sin \left(\frac{\pi}{3}+\alpha\right)$$ (Do not use four different identities to solve this exercise.)

Rewrite each expression in terms of the given function or functions. \(\frac{1-\sin x}{1+\sin x}-\frac{1+\sin x}{1-\sin x} ; \sec x\) and \(\tan x\)

Explain how to verify an identity.

Use an identity to solve each equation on the interval \([0,2 \pi)\) $$ \sin x \cos x=\frac{\sqrt{2}}{4} $$

Describe two strategies that can be used to verify identities.