Maharashtra State BoardHSC Arts 12th Board Exam
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InΔABC with Usual Notations, Prove that 2a {Sin^2(C/2)+Csin^2 (A/2)} = (a + c - b) - Mathematics and Statistics

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In ΔABC with usual notations, prove that 2a `{sin^2(C/2)+csin^2 (A/2)}` = (a +   c - b)

 
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Solution

`sin^2theta =(1-cos2theta)/2`

`L.H.S=2{asin^2(C/2)+csin^2(A/2)}`

`=2{(a(1-cosC))/2+(c(1-cosA))/2}`

=a-acosC+c-ccosA

=(a+c)-(acosC+ccosA)

=a+c-b

R.H.S

2a `{sin^2(C/2)+csin^2 (A/2)}` = (a +   c - b)

Concept: Solutions of Triangle
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