Question

(OR)
sin 2A +sin 2B + sin 2C
A+B+C = 90°. prove that --
sin 2A + sin 2B-sin 2C/sin 2A + sin 2B - sin 2C
=cot A cot B.​

Answer 1

Answer:

sin(A+B)sin(A−B)

=(sinAcosB+cosAsinB)(sinAcosB−cosAsinB)

=(sinAcosB)2−(cosAsinB)2

=sin2Acos2B−cos2Asin2B

=sin2A(1−sin2B)−(1−sin2A)sin2B

=sin2A−sin2Asin2B−sin2B+sin2Asin2B

=sin2A−sin2B