Question

sin2A+sin2B-sin2C=-4sinAsinBcosC​

Answer 1

Answer:

If A+B+C=180 degree, then A+B=180-C hence sin(A+B) = sinC, cos(A+B)=-cosC

sin2A + sin 2B +sin2C

= 2 sin(A+B)cos(A-B) + 2sinC cosC

=2sinC cos(A-B)+2sinC cosC

=2sinC (cos(A-b) + cos C)

=2sin C(cos(A-B) - cos(A+B) )

= 2sinC . 2sin A sin B

=4 sinA sin B sin C