Question

prove that cos (A+B)cos (A-B)= cos2B-sin2A or cos2A-sin2B

Answer 1

we know that (x+y)(x-y) =x^2-y^2
Cos (A+B)=CosAcosB - SinASinB
Cos(A-B) =CosAcosB + SinASinB
Therefore,
Cos^2A + Sin^2A = 1
Cos^2B + Sin^2B = 1
therefore, LHS,
Cos(A+B)(A-B)
= (CosACosB - SinASinB) (CosACosB - SinASinB)
=Cos^ACos^2B - Sin^2A - Sin^2B
= Cos^2B(1-Sin^A) - Sin^2A(1-Cos^B)
= Cos^B - Cos^ASin^2A - Sin^2A + Cos^2BSin^2A
= Cos^B - Sin^2A

HOPE THIS WILL HELP YOU TO SOLVE YOUR QUERY....

Answer 2

Answer:

Here is your answer buddy...