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In any triangle A B C , prove that: acos...

In any triangle `A B C ,` prove that: `acos((B+C)/2)=(b+c)sinA/2`

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`frac{a}{sinA}=frac{b}{sinB}=frac{c}{sinC}=k`
`a=ksinA, b=ksinB, c=ksinC`
`(b+c)(sin)(A/2)=(ksinB+ksinC)sin(A/2)`
`=k(sinB+sinC)sin(A/2)`
`=k(2sin((B+C)/2)cos((B-C)/2))sin(A/2)`
`A+B+C=pi`
`(B+C)/2=(pi/2)-(A/2)`
`sin((B+C)/2)=sin((pi/2)-(A/2))=cos(A/2)` ...
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RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
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  19. In any triangle A B C , prove that following: \ \ a^2sin(B-C)=(b^2-c^2...

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