Question

verify the identity: cos(2x) / sin(x) cos(x) = cot(x) - tan(x)

Answer 1

Working with the right sides:
\[\cot x-\tan x=\frac{\cos x}{\sin x}-\frac{\sin x}{\cos x}\]
Find a common denominator and simplify.
Also, use the fact that \(\cos(2x)=\cos^2x-\sin^2x\).