91Ó°ÊÓ

Determine whether each equation is a conditional equation or an identity. $$\frac{\sqrt{2}}{2}(\sin x+\cos x)=\sin \left(x+\frac{\pi}{4}\right)$$

Use the double-angle identities to verify each identity. $$\frac{1}{2} \sin (4 x)=2 \sin x \cos x-4 \sin ^{3} x \cos x$$

Solve the given trigonometric equation on \(0^{\circ} \leq \theta<360^{\circ}\) and express the answer in degrees to two decimal places. $$\sec \left(\frac{\theta}{2}\right)=1.4275$$

Determine whether each equation is a conditional equation or an identity. $$\cos (2 x)=\cos ^{2} x-\sin ^{2} x$$

Graph the functions. $$y=\sin (2 x) \cos (2 x)$$

Use a calculator to evaluate each expression. Give the answer in radians and round it to two decimal places. $$\tan ^{-1}(1.3242)$$

Verify each of the trigonometric identities. $$\csc (-x)-1=\frac{\cot ^{2} x}{\csc (-x)+1}$$

Use the half-angle identities to find the exact values of the trigonometric expressions. $$\sin \left(\frac{\pi}{8}\right)$$

Verify each of the trigonometric identities. $$\frac{1}{1-\cos x}+\frac{1}{1+\cos x}=2 \csc ^{2} x$$

Determine whether each statement is true or false. $$\sin A \sin B=\sin A B$$