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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

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`R.H.S. = cos(A/2)`
As we know, `A+B+C = 180^@`
`A = 180-(B+C)`
`:.cosA/2 = cos((180-(B+C))/2)=cos(90-(B+C)/2)` As we know, `cos(90-x) = sinx`
`:.cosA/2 = sin((B+C)/2)=L.H.S.`
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