Question

prove that sin 2a=2sina×cosa

Answer 1

sin 2 A

This can also be written as sin ( A + A )

Generally this can be treated like sin ( X + Y )

The trigonometric identity for this is :

sin ( X + Y ) =sin X cos Y + cos X sin Y

Treat X , Y as A :

= sin ( A + A ) = sin A cos A + cos A + sin A

= sin ( 2 A ) = 2 sin A cos A

Hence it is proved .

Also remember that sin ( A - B ) = sin A cos B - cos A sin B

Answer 2

Here is your answer

Question

To prove=>

sin 2a=2sina×cosa

Remember

Sin(x+y) = Sinx × cosy + Siny Cosx

ANSWER

LHS

Sin 2a

=>Sin(A +A)

=> SinACosA + CosASinA

=>2SinACosA

SO. LHS=RHS

HENCE PROVED.

THANKS