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Question

If A,B,C are the interior angles of a Δ ABC, show that:

(i) sin B+C2=cosA2

(ii) cos B+C2=sinA2

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Solution

A+B+C=180

So,

B + C=180-A

B+C2 = 90 - A2 ( Dividing the L.H.S and R.H.S by 2)

sin(B+C2) = sin(90 - A2) ( Substituting B+C2 value)

= cos(A2)


Similarly for second question

cos(90 - A2) = sin(A2)

Hence Proved


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