cos 2x cos 2y + cos^2 (x+y) - cos^2 (x-y) = cos(2x+2y) - Maths - Trigonometric Functions

Question

cos 2x cos 2y + cos^2 (x+y) - cos^2 (x-y) = cos(2x+2y)

Ajanta Trivedi · Accepted Answer

LHS of the given equation is:
cos2x cos2y+cos2(x+y)-cos2(x-y)=12 2cos2x
cos2y+2cos2(x+y)-2cos2(x-y)  [since 2cosAcosB=cos(A+B)+cos(A-B)=12
cos(2x+2y)+cos(2x-2y)+1+cos(2x+2y)-1+cos(2x-2y)  [cos2θ=2cos2θ-1=12
cos(2x+2y)+cos(2x-2y)+1+cos(2x+2y)-1-cos(2x-2y)=12
2cos(2x+2y)=cos(2x+2y)= RHS

hope this helps you