91Ó°ÊÓ

Reducing Powers, use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine. $$\tan ^{2} 2 x \cos ^{4} 2 x$$

Factor the trigonometric expression. There is more than one correct form of each answer. \(6 \cos ^{2} x+5 \cos x-6\)

Solving a Trigonometric Equation In Exercises \(25-38,\) find all solutions of the equation in the interval \(0,2 \pi ) .\) $$2 \sin x+\csc x=0$$

Reducing Powers, use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine. $$\sin ^{2} 2 x \cos ^{2} 2 x$$

Factor the trigonometric expression. There is more than one correct form of each answer. \(\cot ^{2} x+\csc x-1\)

Rewriting a Trigonometric Expression In Exercises \(27-34,\) write the expression as the sine, cosine, or tangent of an angle. $$ \frac{\tan 45^{\circ}-\tan 30^{\circ}}{1+\tan 45^{\circ} \tan 30^{\circ}} $$

Verify the identity. $$\frac{1}{\cos x+1}+\frac{1}{\cos x-1}=-2 \csc x \cot x$$

Solving a Trigonometric Equation In Exercises \(25-38,\) find all solutions of the equation in the interval \(0,2 \pi ) .\) $$\sin x-2=\cos x-2$$

Rewriting a Trigonometric Expression In Exercises \(27-34,\) write the expression as the sine, cosine, or tangent of an angle. $$ \frac{\tan 140^{\circ}-\tan 60^{\circ}}{1+\tan 140^{\circ} \tan 60^{\circ}} $$

Verify the identity. $$\cos x-\frac{\cos x}{1-\tan x}=\frac{\sin x \cos x}{\sin x-\cos x}$$