Anyone help me please 2 \sin7 \alpha. \cos2 \alpha = \sin9 \alpha + \sin5 \alpha ​

Question

Anyone help me please


`2 \sin7 \alpha. \cos2 \alpha = \sin9 \alpha + \sin5 \alpha`
​

Answer 1

Solution,

As we have,

⇒2SinACosB=Sin(A+B)+Sin(A-B)

Now,

`2sin7\alpha .cos2\alpha =sin9\alpha +sin5\alpha \\\\LHS=2sin7\alpha .cos2\alpha \\\\LHS=sin(7\alpha +2\alpha )+sin (7\alpha -2\alpha )\\\\LHS=sin9\alpha +sin5\alpha`

Hence, LHS=RHS