Question

if tan x+ sin x = m and tan x -sin x = n show that (m2-n2)= 16mn​

Answer 1

Answer:

m2-n2=16mn

LHS=(tanx+sinx)2-(tanx-sinx)2

tan2x+sin2x+2sinxtanx-tan2x-sin2x+2sinxtanx

4sinxtanx

now,

RHS=16{tan2x-sin2x}

again,

4sinxtanx=16tan2x-sin2x