A) independent of A, B,
B) function of A, B
C) function of C
D) none of these
Correct Answer: A
Solution :
[a] \[=\] \[2\sin \frac{A}{2}\cos ec\frac{B}{2}\left( \sin \frac{C}{2}-\cos \frac{A}{2}\cos \frac{B}{2} \right)-\cos A\] \[=2\sin \frac{A}{2}\cos ec\frac{B}{2}\times \left( \cos \frac{A+B}{2}-Cos\frac{A}{2}\cos \frac{B}{2} \right)-\cos A\] \[=\] \[2\sin \frac{A}{2}\cos ec\frac{B}{2}\times \left( -\sin \frac{A}{2}\sin \frac{B}{2} \right)-\cos A\] \[=-2{{\sin }^{2}}\frac{A}{2}-\cos A=-1\]
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