Question

Prove the following:

`(sin3x)/cosx + (cos3x)/sinx` = 2 cot 2x

Answer 1

L.H.S. = `(sin3x)/cosx + (cos3x)/sinx`

= `(sin3x*sinx + cos3x*cosx)/(sinx*cosx)`

= `(cos(3x - x))/(sinx*cosx)`

= `(2cos2x)/(2sinx*cosx)`

= `(2cos2x)/(sin2x)`

= 2 cot 2x

= R.H.S.