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With usual notation prove that 2 ( a sin^2 C/2+c sin^2 A/2 ) = a + c- b

 

With usual notation prove that 2 ( a sin^2 C/2+c sin^2 A/2 ) = a + c- b

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
576-367_1.PNG
Vikas TU
14149 Points
one year ago
Dear student 
2(a.sin^2C/2+c.sin^2 A/2)=c+a-b
L.H.S.
=2(a.sin^2 C/2+c.sin^2 A/2). , we know that cosx=1–2.sin^2 x/2
or sin^2 x/2=(1-cosx)/2.
=2.[a.(1-cosC)/2+c.(1-cosA)/2]
=a.(1-cosC)+c.(1-cosA).
=a-a.cosc+c-c.cosA
=a-(a.cosC+c.cosA)+c. , putting a.cosC+c.cosA = b.
=a-b+c. Proved.

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