91Ó°ÊÓ

Prove the identity. $$2 \sin ^{2} \theta \cos ^{2} \theta+\cos ^{4} \theta=1-\sin ^{4} \theta$$

Use a graphing calculator to determine which of the following expressions asserts an identity. Then derive the identity algebraically.\(2 \cos ^{2} \frac{x}{2}=\cdots\) a) \(\sin x(\csc x+\tan x) b) \)\sin x-2 \cos x\( c) \)2\left(\cos ^{2} x-\sin ^{2} x\right)\( d) \)1+\cos x$

Simplify and check using a graphing calculator. $$\frac{\sin ^{2} \theta-9}{2 \cos \theta+1} \cdot \frac{10 \cos \theta+5}{3 \sin \theta+9}$$

Use a calculator to find each of the following in radians, rounded to four decimal places, and in degrees, rounded to the nearest tenth of a degree. $$\sec ^{-1} 1.1677$$

Prove the identity. $$\frac{\cot \theta}{\csc \theta-1}=\frac{\csc \theta+1}{\cot \theta}$$

Use a graphing calculator to determine which of the following expressions asserts an identity. Then derive the identity algebraically. \frac{\sin 2 x}{2 \cos x}=\cdots a) \(\cos x\) b) \(\tan x\) c) \(\cos x+\sin x\) d) \(\sin x\)

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

Use a calculator to find each of the following in radians, rounded to four decimal places, and in degrees, rounded to the nearest tenth of a degree. $$\tan ^{-1}(1.091)$$

Use a calculator to find each of the following in radians, rounded to four decimal places, and in degrees, rounded to the nearest tenth of a degree. $$\cot ^{-1} 1.265$$

Simplify and check using a graphing calculator. $$\frac{9 \cos ^{2} \alpha-25}{2 \cos \alpha-2} \cdot \frac{\cos ^{2} \alpha-1}{6 \cos \alpha-10}$$