Question

$\text{In triangle ABC, internal angle bisector of}\angle A\text{makes an angle}\theta \text{with side BC}.\text{Value of sin}\theta \text{is equal to}$

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$\theta =B+\frac{A}{2}=\pi -(C+\frac{A}{2})\Rightarrow sin\theta =sin(B+\frac{A}{2})=sin(C+\frac{A}{2})=sin(B+\frac{\pi }{2}-\frac{B+C}{2})=sin(C+\frac{\pi }{2}-\frac{B+C}{2})$

$=cos\left(\frac{B-C}{2}\right)$