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Question

In ABC, sin(AB)sin(A+B)=
[MP PET 1986]

A
a2b2c2
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B
a2+b2c2
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C
c2a2b2
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D
c2a2+b2
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Solution

The correct option is A a2b2c2
sin(AB)sin(A+B=sin A cos Bsin B cos Asin C
=accos BbccosA
But cos B=a2+c2b22ac,cos A=b2+c2a22bc
accosBbccosA=12c2
(a2+c2b2b2c2+a2)=a2b2c2

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