Question

prove that sinA.sin2A+sin3A. sin6A/sinA.cos2A+sin3A.cos6A=tan5A

Answer 1

(sinAsin2A + sin3Asin6A)

sinAcos2A + sin3Acos6A

2sinAsin2A + 2sin3Asin6A)

2sinAcos2A + 2sin3Acos6A

cosA - cos3A + cos3A - cos9A

sin3A - sinA + sin9A - sin3A

cosA - cos9A

sin9A - sinA

2 sin (A+9A)/2 sin(9A-A)/2

2 cos(9A+A)/2sin(9A-A)/2

sin5A sin4A

cos5A sin4A

= tan 5A

proved