Question

How do I verify the identity of the following trigonometric function?

Answer 1

See below

Explanation:

From the double angle identities

`sin(2x) = 2 sin x cos x`

and

`cos(2x) = cos^2 x-sin^2 x = 2cos^2 x-1`

we have

`(1+cos(2x))/sin(2x) = (2cos^2 x-1+1)/(2sin x cos x) = (2 cos^2 x)/(2 sin x cos x)`
`qquad = cosx/sinx=cot x`