Question

Show that (sin theta +cos theta)– (sin theta – cos theta)^2 = 2 sin 2theta.​

Answer 1

Step-by-step explanation:

R.T.P: (sinθ+cosθ)2+(sinθ−cosθ)2=2

LHS:-

(sinθ+cosθ)2+(sinθ−cosθ)2

⟹(sin2θ+cos2θ+2sinθcosθ+sin2θ+cos2θ−2sinθcosθ)

⟹(sin2θ+cos2θ+sin2θ+cos2θ)

=(1+1)

=2

RHS:-

2

∴ LHS = RHS

Hence, it is proved.