In a ∆ABC, if sin A and sin B are the roots of the equation c²x² – c (a + b) x + ab = 0, then find ∠C.

Question

In a ∆ABC, if sin A and sin B are the roots of the equation c 2 x 2 – c (a + b) x + ab = 0, then find ∠ C.

Philoid · Accepted Answer

According to the product of the roots

But by sine law we know,

and

So,

Therefore,

So,

sin C=1

C=90°

In a ∆ABC, if sin A and sin B are the roots of the equation c2x2 – c (a + b) x + ab = 0, then find ∠C.