Question

(Sinx + cosx) ÷ cos^3x = tan^3x + tan^2x + tanx + 1 ; prove LHS = RHS

Answer 1

LHS= (sinx +cosx)/cos^3x
=sec^2xtanx+sec^2x
=sec^2x(tanx+1)------(1)

RHS=tan^3x +tan^2x+tanx +1
=tanx + tan^3x +1+tan^2x
=tanx(1+ tan^2x)+ 1+ tan^2x
=tanxsec^2x+sec^2x
=sec^2x(tanx+1)----(2)

From (1) and (2)
LHS=RHS