Question

A B & C are interior angles of triangle ABC. Show that

1) sin(B+C)/2= cosA/2

2) If A = 90 degrees, then find the value of tan(B+C/2)

Answer 1

Step-by-step explanation:

(i)

Given: A,B,C are interior angles.

So, A + B + C = 180°

⇒ (A + B + C)/2 = 180/2

⇒ (A + B + C)/2 = 90°

⇒ (A/2) + (B + C)/2 = 90°

⇒ (B + C)/2 = 90° - (A/2)

LHS:

sin(B + C)/2

= sin(90 - A/2)

= cos A/2

(2)

Given A = 90°.

= tan(B + C)/2

= tan(90 - A/2)

= cotA/2

= cot 45

= 1.

Hope it helps!