Question

sin 38° + sin 22° = sin 82°​

Answer 1

Answer:

Step-by-step explanation:

Given :

To prove :

sin 38° + sin 22° = sin 82°​

Solution :

We know that,

$sinA + sinB=2sin(\frac{A+B}{2})cos(\frac{A-B}{2})$

LHS = sin 38° + sin 22°

⇒ $2sin(\frac{38+22}{2})cos(\frac{38-22}{2})$

⇒ $2sin(\frac{60}{2})cos(\frac{16}{2})$

⇒ $2(sin \ 30)(cos \ 8)$

⇒ $2(\frac{1}{2})(cos \ 8)$

⇒ $cos \ 8$

⇒ $cos \ (90 - 82)$

⇒ $sin \ 82$ = RHS

Hence, Proved,.