91Ó°ÊÓ

Perform the addition or subtraction and use the fundamental identities to simplify. There is more than one correct form of each answer. \(\frac{1}{1+\cos x}+\frac{1}{1-\cos x}\)

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

Perform the addition or subtraction and use the fundamental identities to simplify. There is more than one correct form of each answer. \(\frac{1}{\sec x+1}-\frac{1}{\sec x-1}\)

Verify the identity. $$\sec ^{2}\left(\frac{\pi}{2}-x\right)-1=\cot ^{2} x$$

Finding \(x\) -lntercepts In Exercises \(45-48,\) find the \(x\) -intercepts of the graph. $$y=\sin \pi x+\cos \pi x$$

Finding \(x\) -lntercepts In Exercises \(45-48,\) find the \(x\) -intercepts of the graph. $$y=\tan ^{2}\left(\frac{\pi x}{6}\right)-3$$

Verify the identity. $$\tan \left(\sin ^{-1} x\right)=\frac{x}{\sqrt{1-x^{2}}}$$

Perform the addition or subtraction and use the fundamental identities to simplify. There is more than one correct form of each answer. \(\tan x-\frac{\sec ^{2} x}{\tan x}\)

Solving a Trigonometric Equation, find all solutions of the equation in the interval\(0,2 \pi\) ). Use a graphing utility to graph the equation and verify the solutions. $$\cos \frac{x}{2}-\sin x=0$$

Verify the identity. $$\cos \left(\sin ^{-1} x\right)=\sqrt{1-x^{2}}$$