What is the value of the expression $\cos 2 A \cos 2 B+\sin ^2(A-B)-\sin ^2(A+B)$ ?
Answer & explanation
Correct answer: option 3
cos 2A . cos 2B + sin² ( A - B ) - sin² ( A + B )
= cos 2A . cos 2B - [ sin² ( A + B ) + sin² ( A - B ) ]
{ we know, sin² x - sin² y = sin(x + y). sin( x - y) }
= cos 2A . cos 2B - [ sin ( A + B + A - B ) .sin( A + B - A + B ) ]
= cos 2A . cos 2B - sin 2A .sin 2B
{ using , cos ( x + y ) = cos x. cos y - sin x. sin y
= cos ( 2A + 2B )