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If $0 < A < \frac{π}{6}$ and $\sin A + \cos A = \frac{\sqrt{7}}{2}$ , then $\tan \frac{A}{2} =$

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a

7−23

b

7+23

c

73

d

none of these

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detailed solution

Correct option is A

We have,sin⁡A+cos⁡A=72⇒2tan⁡A21+tan2⁡A2+1−tan2⁡A21+tan2⁡A2=72⇒4tan⁡A2+2−2tan2⁡A2=7+7tan2⁡A2⇒(7+2)tan2⁡A2−4tan⁡A2+(7−2)=0⇒tan⁡A2=4±16−4(7+2)(7−2)2(7+2)⇒ tan⁡A2=4±22(7+2)⇒ tan⁡A2=37+2,17+2⇒ tan⁡A2=7−2,7−23⇒ tan⁡A2=7−23 ∵0

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