The Total solution for NCERT class 6-12
cos2 (π/4– x) – sin2 (π/4 – x) = sin 2x
Let us consider LHS:
cos2 (π/4 – x) – sin2 (π/4– x)
We know, cos2 A – sin2 A= cos 2A
So,
cos2 (π/4 – x) – sin2 (π/4– x) = cos 2 (π/4 – x)
= cos (π/2 – 2x)
= sin 2x [since, cos (π/2 – A) = sin A]
= RHS
Hence proved.