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If A, B and C are interior angles of a t...

If A, B and C are interior angles of a triangle ABC, then show that `"sin"((B+C)/2)=cos(A/2)` .

Text Solution

Verified by Experts

In `deltaABC`
`A+B+C=180^(@)`
`rArrB+C=180^(@)-A`
`rArr(B+C)/(2)=90^(@)-(A)/(2)`
`rArr"sin" (B+C)/(2)=sin(90^(@)-(A)/(2))`
`rArr"sin"(B+C)/(2)="cos"(A)/(2)`
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