Question -
Answer -
We know that, for a given triangle, sum of allthe interior angles of a triangle is equal to 180°
A + B + C = 180° ….(1)
To find the value of (B+ C)/2, simplify theequation (1)
⇒ B + C = 180° – A
⇒ (B+C)/2 = (180°-A)/2
⇒ (B+C)/2 = (90°-A/2)
Now, multiply both sides by sin functions, weget
⇒ sin (B+C)/2 = sin (90°-A/2)
Since sin (90°-A/2) = = cos A/2, the aboveequation is equal to
sin (B+C)/2 = cos A/2
Hence proved.