Question

Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`

Answer 1

RHS = `(2 cos^3 theta - cos theta) tan theta`

        =`(2 cos^2 theta - 1) cos theta xx sin theta/ cos theta`

       =`[2(1- sin^2 theta ) -1] sin theta`

       =` (2-2 sin^2 theta -1 ) sin theta`

       =` (1-2 sin^2 theta ) sin theta`

       =`( sin theta -2 sin^3 theta )`

      =LHS