# A, B and C are interior angles of a triangle ABC. Show that sin (("B"+"C")/2) = cos  "A"/2 - Mathematics

Sum

A, B and C are interior angles of a triangle ABC. Show that

sin (("B"+"C")/2) = cos  "A"/2

#### Solution

We know that for a triangle ABC,

∠A + ∠B + ∠C = 180°

∠B + ∠C = 180° − ∠A

(angle "B" +angle "C")/2 = 90° - (angle"A")/2

((sin "B+C")/2) = sin (90°- "A"/2)

= cos ("A"/2)

Concept: Trigonometric Ratios of Complementary Angles
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