Question

If A , B and C are interior angles of a triangle ABC , then show that.​

Answer 1

Answer:

We know that, for a given triangle, the sum of all the interior angles of a triangle is equal to 180°

A + B + C = 180° …………………..(1)

To find the value of (B + C)/2, simplify the equation (1)

⇒ B + C = 180° – A

⇒ (B + C)/2 = (180° – A)/2

⇒ (B + C)/2 = 90° – A/2

Now, multiply both sides by sin functions, we get

⇒ sin (B+C)/2 = sin (90°-A/2)

sin (90°-A/2) = cos A/2

The above equation is equal to

sin (90° – A/2) = sin A/2

sin (B + C)/2 = cos A/2

Hence proved.