91Ó°ÊÓ

Simplify each of the trigonometric expressions. $$\left(\sin ^{2} x\right)\left(\cot ^{2} x+1\right)$$

Write each expression as a product of sines and/or cosines. $$\sin (0.4 x)+\sin (0.6 x)$$

Find the exact value of each expression. Give the answer in degrees. $$\operatorname{arccot} 1$$

Write each expression as a single trigonometric function. $$\frac{\tan 49^{\circ}+\tan 23^{\circ}}{1-\tan 49^{\circ} \tan 23^{\circ}}$$

Use the double-angle identities to verify each identity. $$(\sin x+\cos x)^{2}=1+\sin (2 x)$$

Solve the given trigonometric equation exactly on \(0 \leq \theta<2 \pi\). $$\tan ^{2} \theta-1=0$$

Simplify the trigonometric expressions. $$\frac{\cos (3 x)-\cos x}{\sin (3 x)+\sin x}$$

Solve the given trigonometric equation exactly on \(0 \leq \theta<2 \pi\). $$2 \cos ^{2} \theta-\cos \theta=0$$

Simplify each of the trigonometric expressions. $$1-\frac{\sin ^{2} x}{1-\cos x}$$

Verify the identities. $$\frac{\cos A-\cos B}{\sin A+\sin B}=-\tan \left(\frac{A-B}{2}\right)$$