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CBSE Class 10 Answered

Sin^2A/2+Sin^2(B+C/2)
Asked by adinaditi29 | 14 Mar, 2022, 12:02: PM
answered-by-expert Expert Answer
The question must be:
In triangle ABC, show that sin2A/2 = sin2(B+C)/2 = 1
 
Solution:

In a triangle sum of all angles is 180 degrees.

A + B + C = 180o

B + C = 180 - A

B + C/2 = 90 - A/2

sin2 (B + C/2) = sin2 (90 - A/2)

sin2 (B + C/2) = cos2 A/2

Hence, LHS = sin2 A/2 + sin2 (B + C/2) = sin2 A/2 + cos2 A/2 = 1

Answered by Renu Varma | 16 Mar, 2022, 10:38: AM

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