Question

How do you prove that `(2sinx)/[secx(cos4x-sin4x)]=tan2x`?

Answer 1

As proved

Explanation:

I suppose the sum is

`(2 sin x) / (sec x (cos^4 x - sin ^4 x)) = tan 2x`

`=> (2 sin x cos x) / ((cos^2 x + sin-^2x)* (cos ^2x - sin^2x))`

`color(crimson)(sin 2x = 2 sin x cos x`, identity

`color(crimson)(cos^2 x + sin ^2 x -= 1`, identity

`color(crimson)(cos^2x - sin^2 x = cos 2x`, identity

`:. => (sin 2x) / (cos 2x) = tan 2x = R H S`