91Ó°ÊÓ

Find all solutions of the equation \(2 \sin x=1-\cos x\) in the interval \(0^{\circ} \leq x<360^{\circ} .\) Use a calculator and round the answer(s) to one decimal place.

Find all solutions of the equation \(\cos (x / 2)=1+\cos x\) in the interval \(0 \leq x<2 \pi\).

Use graphs to determine whether there are solutions for each equation in the interval \([0,1] .\) If there are solutions, use the graphing utility to find them accurately to two decimal places. (a) \(1 /\left(\tan ^{-1} x+\sin ^{-1} x\right)=\sin 2 x\) (b) \(1 /\left(\tan ^{-1} x+\sin ^{-1} x\right)=\sin 3 x\)

Prove the identities. $$\frac{\sin (A+B)}{\sin (A-B)}=\frac{\tan A+\tan B}{\tan A-\tan B}$$

Prove the identities. $$\frac{\cos (A+B)}{\cos (A-B)}=\frac{1-\tan A \tan B}{1+\tan A \tan B}$$

Find all solutions of the equation $$ \sin 3 x \cos x+\cos 3 x \sin x=\frac{\sqrt{3}}{2} $$ in the interval \(0

Use graphs to determine whether there are solutions for each equation in the interval \([0,1] .\) If there are solutions, use the graphing utility to find them accurately to two decimal places. (a) \(1 /\left(\sin ^{-1} x+\cos ^{-1} x\right)=4 x^{3}\) (b) \(1 /\left(\sin ^{-1} x+\cos ^{-1} x\right)=5 x^{3}\)

Find all real numbers \(\theta\) for which $$ \sec 4 \theta+2 \sin 4 \theta=0 $$

Use graphs to determine whether there are solutions for each equation in the interval \([0,1] .\) If there are solutions, use the graphing utility to find them accurately to two decimal places. $$\sin ^{-1} x=\cos ^{-1} x$$

Consider the equation \(\sin ^{2} x-\cos ^{2} x=7 / 25\) (a) Solve the equation for \(\cos x\) (b) Find all of the solutions of the equation satisfying \(0