Question

show that (sin theta+cos theta)^2 - (sin theta - cos theta)^2=2sin2theta​

Answer 1

Answer:

Step-by-step explanation:

(sinθ+cosθ)^2-(sinθ-cosθ)^2

=sin^2θ+cos^2θ+2sinθcosθ-(sin^2θ+cos^2θ)+2sinθcosθ

=4sinθcosθ                                                                    (sin^2θ+cos^2θ=1)

=2sin2θ                                                                           (2sinθcosθ=sin2θ)