Question

Simplify sin X (1 + cot2 X ).

Answer 1

\[\sin x \left( 1+\cot 2x \right)=\sin x \left( 1+\frac{ \cos 2x }{\sin 2x } \right)\]
\[=\sin x \frac{ \sin 2x+\cos 2x }{\sin 2x }=\sin x \frac{ 2\sin x \cos x+\cos ^{2}x-\sin ^{2} x }{2\sin x \cos x }\]
\[=\frac{ 2\sin x \cos x+\cos ^{2}x-\sin ^{2}x }{2\cos x }\]

Answer 2

is that cot(2x) or cot^2 (x) ?

Answer 3

X= theta