Question

Prove this for helping me please

Answer 1

If we take R.H.S. =>

R.H.S. = (cos x + sin x)/(cos x - sin x) - (cos x - sin x)/(cos x + sin x)

= {(cos x + sin x)^2 - (cos x - sin x)^2} / (cos x + sin x)(cos x - sin x).........................................(equating the denominator.)

= { (cos^2x + sin^2x + 2sin x.cos x) - (cos^2x + sin^2x - 2sin x.cos x) } / (cos^2x - sin^x)

= (1 + 2sin x.cos x - 1 + 2sin x.cosx) / cos2x.............(cos^2x - sin^2x = cos2x)

= (sin2x + sin2x) / cos2x......................(2sin x.cos x = sin2x)

= 2(sin2x/cos2x)

R.H.S.= L.H.S. = 2tan2x........●

Hence Proved.

Hope it was helpful.