Question

Sin2A+Sin2B+Sin2(A-B) = 4sina.cosb.cos(a-b)​

Answer 1

Step-by-step explanation:

(sin2a+sin2b)+sin2(a-b)

={2sin((2a+2b)/2)cos((2a-2b)/2)}+sin2(a-b)

=2sin(a+b)cos(a-b)+sin2(a-b)

=2sin(a+b)cos(a-b)+2sin(a-b)cos(a-b)

=2cos(a-b) {sin(a+b) + sin(a-b)}

=2cos(a-b).{2sinacosb}

=4sina.cosb.cos(a-b) [proved]