91Ó°ÊÓ

In Exercises 57-60, perform the multiplication and use the fundamental identities to simplify. There is more than one correct form of each answer. $$ (\cot x+\csc x)(\cot x-\csc x) $$

In Exercises 55-64, verify the identity. $$ \cos \left(\frac{5 \pi}{4}-x\right)=-\frac{\sqrt{2}}{2}(\cos x+\sin x) $$

The equation \(1+\tan ^{2} \theta=1+\cot ^{2} \theta\) is not an identity, because it is true that \(1+\tan ^{2}(\pi / 6)=1 \frac{1}{3}\), and \(1+\cot ^{2}(\pi / 6)=4\)

In Exercises 57-60, perform the multiplication and use the fundamental identities to simplify. There is more than one correct form of each answer. $$ (2 \csc x+2)(2 \csc x-2) $$

In Exercises 59-62, use inverse functions where needed to find all solutions of the equation in the interval \([0,2 \pi)\). $$ \tan ^{2} x-6 \tan x+5=0 $$

In Exercises 59-62, find all solutions of the equation in the interval \([0,2 \pi\) ). Use a graphing utility to graph the equation and verify the solutions. $$ \sin \frac{x}{2}+\cos x=0 $$

In Exercises 55-64, verify the identity. $$ \cos (\pi-\theta)+\sin \left(\frac{\pi}{2}+\theta\right)=0 $$

In Exercises 59-62, use inverse functions where needed to find all solutions of the equation in the interval \([0,2 \pi)\). $$ \sec ^{2} x+\tan x-3=0 $$

In Exercises 57-60, perform the multiplication and use the fundamental identities to simplify. There is more than one correct form of each answer. $$ (3-3 \sin x)(3+3 \sin x) $$

In Exercises 59-62, find all solutions of the equation in the interval \([0,2 \pi\) ). Use a graphing utility to graph the equation and verify the solutions. $$ \sin \frac{x}{2}+\cos x-1=0 $$