Question

If sin 80 + sin 50= 2 sin a sin b find a,b.

Answer 1

Step-by-step explanation:

We have,

$\sin(80\degree) + \sin(50\degree) = 2 \sin(a) \sin(b)$

$\implies2\sin \left( \dfrac{80\degree +50\degree}{2} \right) \cos\left( \dfrac{80\degree - 50\degree}{2} \right) = 2 \sin(a) \sin(b)$

$\implies2\sin \left( \dfrac{130\degree }{2} \right) \cos\left( \dfrac{30\degree }{2} \right) = 2 \sin(a) \sin(b)$

$\implies2\sin \left( 75\degree \right) \cos\left(15\degree \right) = 2 \sin(a) \sin(b)$

$\implies2\sin \left( 75\degree \right) \sin\left(90 \degree - 15\degree \right) = 2 \sin(a) \sin(b)$

$\implies2\sin \left( 75\degree \right) \sin\left(75\degree \right) = 2 \sin(a) \sin(b)$

On comparing, a = 75° and b = 75°