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Question: In any triangle \(ABC\sin^{2}\frac{A}{2} + \sin^{2}\frac{B}{2} + \sin^{2}\frac{C}{2}\) is equal to...

In any triangle ABCsin⁡2A2+sin⁡2B2+sin⁡2C2ABC\sin^{2}\frac{A}{2} + \sin^{2}\frac{B}{2} + \sin^{2}\frac{C}{2} is equal to

A

1−2cos⁡A2cos⁡B2cos⁡C21 - 2\cos\frac{A}{2}\cos\frac{B}{2}\cos\frac{C}{2}

B

1−2sin⁡A2cos⁡B2cos⁡C21 - 2\sin\frac{A}{2}\cos\frac{B}{2}\cos\frac{C}{2}

C

1−2sin⁡A2sin⁡B2sin⁡C21 - 2\sin\frac{A}{2}\sin\frac{B}{2}\sin\frac{C}{2}

D

1−2cos⁡A2cos⁡B2sin⁡C21 - 2\cos\frac{A}{2}\cos\frac{B}{2}\sin\frac{C}{2}

Answer

1−2sin⁡A2sin⁡B2sin⁡C21 - 2\sin\frac{A}{2}\sin\frac{B}{2}\sin\frac{C}{2}

Explanation

Solution

Sol. Trick: For A=B=C=60oA = B = C = 60^{o} only option (3) satisfies the

condition.