91Ó°ÊÓ

Verify that each equation is an identity. $$\frac{\cos (A-B)}{\cos A \sin B}=\tan A+\cot B$$

Use an identity to write each expression as a single trigonometric function value. $$\sqrt{\frac{1-\cos 147^{\circ}}{1+\cos 147^{\circ}}}$$

Give solutions over the interval \([0,2 \pi)\) as approximations to the nearest hundredth when exact values cannot be determined. You may need to use the quadratic formula. Give approximate answers in Exercises \(59-64\) to the nearest tenth of a degree over the interval \(\left[0^{\circ}, 360^{\circ}\right)\) $$\tan ^{2} x+4 \tan x+2=0$$

Verify that each equation is an identity. $$\frac{\sin (A+B)}{\cos A \cos B}=\tan A+\tan B$$

Give solutions over the interval \([0,2 \pi)\) as approximations to the nearest hundredth when exact values cannot be determined. You may need to use the quadratic formula. Give approximate answers in Exercises \(59-64\) to the nearest tenth of a degree over the interval \(\left[0^{\circ}, 360^{\circ}\right)\) $$3 \cot ^{2} x-3 \cot x=1$$

Use an identity to write each expression as a single trigonometric function value. $$\sqrt{\frac{1+\cos 165^{\circ}}{1-\cos 165^{\circ}}}$$

Write expression in terms of sine and cosine, and simplify it. (The final expression does not have to be in terms of sine and cosine.) $$\frac{1+\tan ^{2} \theta}{1+\cot ^{2} \theta}$$

Use a calculator to give each real-number value of \(y .\) $$y=\arcsin 0.92837781$$

Write expression in terms of sine and cosine, and simplify it. (The final expression does not have to be in terms of sine and cosine.) $$\sin \theta(\csc \theta-\sin \theta)$$

Verify that each equation is an identity. $$\frac{\sin (A-B)}{\sin B}+\frac{\cos (A-B)}{\cos B}=\frac{\sin A}{\sin B \cos B}$$