Question

Prove the identity (sin3A+sinA)/2sin2A= cosA​

Answer 1

Step-by-step explanation:

$\frac{ \sin(3A) + \sin(A) }{2 \sin(2A) }$

Using the trigonometric identity

$\sin(x) + \sin(y) = 2 \sin( \frac{x + y}{2} ) \cos( \frac{x - y}{2} )$

Rewrite the expression

We have

$\frac{2 \sin(2A) \cos(A) }{2 \sin(2A) }$

Reduce the fraction with 2

That's

$\frac{ \sin(2A) \cos(A) }{ \sin(2A) }$

Reduce the fraction with sin 2A

We have the final answer as

cos A

As proven

Hope this helps you