Question

सिद्ध कीजिए कि sin 8A+ sin 2a = 2 sin 5a cos 3a

Answer 1

2sin 5A cos 3A - sin8A
=2sin 5A cos 3A - sin (5A+3A)
note: sin(X+Y)=sinX cosY + cosX sinY
=2sin5A cos 3A -[sin5A cos 3A+cos 5A sin 3A]
=2sin 5A cos 3A -[sin5A cos3A + cos5A sin3A]
=2sin5A cos3A - sin5A cos 3A - cos5A sin3A
=sin5A cos3A - cos5A sin3A
note=sin(x - y)=sinX cosY - cosX sinY
= sin(5A - 3A)
= sin2A

I hope this answers help you