91Ó°ÊÓ

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

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

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

Write a short paper in your own words explaining to a classmate the difference between a trigonometric identity and a conditional equation. Include suggestions on how to verify a trigonometric identity.

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

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the given interval. $$2 \sec ^{2} x+\tan x-6=0, \quad\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$$

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

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

(a) use a graphing utility to graph the function and approximate the maximum and minimum points on the graph in the interval \([0,2 \pi),\) and (b) solve the trigonometric equation and demonstrate that its solutions are the \(x\) -coordinates of the maximum and minimum points of \(f .\) (Calculus is required to find the trigonometric equation.) Function $$f(x)=\sin ^{2} x+\cos x$$ Trigonometric Equation $$2 \sin x \cos x-\sin x=0$$

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