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If A,B,C are the angles of a triangle and $c os B + \cos C = 4 \sin^{2} \frac{A}{2}$ , then $\tan \frac{B}{2} \tan \frac{C}{2}$ is equal to

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a

1/2

b

1/3

c

2/3

d

3/2

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detailed solution

Correct option is B

cos⁡B+cos⁡C=4sin2⁡(A/2)⇒ 2cos⁡B+C2cos⁡B−C2=4sin⁡A2sin⁡π2−B+C2⇒ 2sin⁡A2cos⁡B−C2=4sin⁡A2cos⁡B+C2⇒ cos⁡B2cos⁡C2+sin⁡B2sin⁡C2=2cos⁡B2cos⁡C2−sin⁡B2sin⁡C2⇒3sin⁡B2sin⁡C2=cos⁡B2cos⁡C2⇒tan⁡B2tan⁡C2=13.

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