Question

Complete the following

\(\bigtriangleup\)ABC cos(B + C)/2 = ? 

1. Cos A
2. SinA/2
3. Sin A + B /2
4. Cot B 

Answer 1

Correct Answer - Option 2 : SinA/2

Given:

In triangle ABC, cos(B + C)/2 = ?

Concept used:

Angle Sum Property of triangle: The sum of 3 angles of a triangle is 180° 

Calculation:

We know, A + B + C = 180°    (1)

Dividing the equation (1) by 2 

⇒ (A + B + C)/2 = 90° 

⇒ A/2 + (B + C)/2 = 90° 

⇒ (B + C)/2 = 90° - A/2 

By taking cos on both sides, we get:

⇒ cos(B + C)/2 = cos(90° - A/2)       {cos(90° - θ) = sinθ}

∴ cos(B + C)/2 = sinA/2