91Ó°ÊÓ

Verify the identity. $$\frac{1+\sin x}{1-\sin x}=(\tan x+\sec x)^{2}$$

Which of the following statements is true? A. Every identity is an equation. B. Every equation is an identity. Give examples to illustrate your answer. Write a short paragraph to explain the difference between an equation and an identity.

Verify the identity. $$\frac{\tan x+\tan y}{\cot x+\cot y}=\tan x \tan y$$

Verify the identity. $$(\tan x+\cot x)^{4}=\csc ^{4} x \sec ^{4} x$$

Verify the identity. $$(\sin \alpha-\tan \alpha)(\cos \alpha-\cot \alpha)=(\cos \alpha-1)(\sin \alpha-1)$$

Make the indicated trigonometric substitution in the given algebraic expression and simplify (see Example 7 ). Assume \(0 \leq \theta<\pi / 2.\) $$\frac{x}{\sqrt{1-x^{2}}}, \quad x=\sin \theta$$

If \(A, B,\) and \(C\) are the angles in a triangle, show that $$\sin 2 A+\sin 2 B+\sin 2 C=4 \sin A \sin B \sin C$$

Make the indicated trigonometric substitution in the given algebraic expression and simplify (see Example 7 ). Assume \(0 \leq \theta<\pi / 2.\) $$\sqrt{1+x^{2}}, \quad x=\tan \theta$$

Make the indicated trigonometric substitution in the given algebraic expression and simplify (see Example 7 ). Assume \(0 \leq \theta<\pi / 2.\) $$\sqrt{x^{2}-1}, \quad x=\sec \theta$$

Make the indicated trigonometric substitution in the given algebraic expression and simplify (see Example 7 ). Assume \(0 \leq \theta<\pi / 2.\) $$\frac{1}{x^{2} \sqrt{4+x^{2}}}, x=2 \tan \theta$$