91Ó°ÊÓ

Consider the equation \(\frac{\sin 2 x}{1-\cos 2 x}=\cot x\) a) Determine the non-permissible values for \(x\) b) Prove that the equation is an identity for all permissible values of \(x\)

If the point (2,5) lies on the terminal arm of angle \(x\) in standard position, what is the value of \(\cos (\pi+x) ?\)

Solve \(4 \sin ^{2} x=3 \tan ^{2} x-1\) algebraically. Give the general solution expressed in radians.

Find the general solution for the equation \(4\left(16^{\cos ^{2} x}\right)=2^{6 \cos x} .\) Give your answer in radians.

Use a double-angle identity for cosine to determine the half-angle formula for cosine, \(\cos \frac{x}{2}=\pm \sqrt{\frac{1+\cos x}{2}}\).