Question

Prove that.. Cos^2A+sin^2A. Cos2B=cos^2B+sin^2B. Cos2A

Answer 1

L.H.S=cos^2A+sin^2A.cos2B
=cos^2A+sin^2A.(1-2sin^2B) [ since,
cos2A=1-2sin^2A]
=cos^2A+sin^2A-2.sin^2A.sin^2B
=1-2.sin^2A.sin^2B [ since, sin^2A+cos^2A=1]
R. H. S=cos^2B+sin^2B.cos2A
=cos^2B+sin^2B.(1-2sin^2A)
=cos^2B+sin^2B-2.sin^2A.sin^2B
=1-2.sin^2A.sin^2B
L. H. S=R.H.S
hence proved