Question

Hey friends plzz help me 18th question. Don't spam

Answer 1

Given Equation is cos^2A + cos^2B - 2cosAcosB(A + B)

= > cos^2A + cos^2B - 2cosAcosB[cosAcosB - sinAsinB]

= > cos^2A + cos^2B - 2cos^2Acos^2B + 2cosAcosBsinAsinB

= > cos^2A + cos^2B - cos^2Acos^2B - cos^2Acos^2B + 2cosAcosBsinAsinB

= > cos^2A - cos^2Acos^2B + cos^2B - cos^2Acos^2B + 2cosAcosBsinAsinB

= > cos^2A(1 - cos^2B) + cos^2B(1 - cos^2A) + 2cosAcosBsinAsinB

= > cos^2Asin^2B + cos^2Bsin^2A + 2cosAcosBsinAsinB

We know that sin(A + B) = sinAcosB + cosAsinB

= > sin^2(A + B).

Hope this helps!