Question

prove the following identity:
cos 2x+cos x+1/sin 2x+sin x=cot x
thanks

Answer 1

\[cos2x+cos x+1/sin2x+sin x=cot x\]

Answer 2

Simplifying the function and using trigonometric identities, you can prove the identity.

Answer 3

Tis is what you wrote:

\( \cos2x+\cos x+\dfrac{1}{\sin2x}+\sin x=\cot x\)

You can't prove that identity because it isn't one.

Did you mean this?

\( \dfrac{\cos2x+\cos x+1}{\sin2x+\sin x} = \cot x \)

Answer 4

yes it is

Answer 5

Here are two identities that may be useful.

\(\cos 2x = \cos^2 x - sin^2 x\)

\(\sin 2x = 2 \sin x \cos x\)

Answer 6

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