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Question: If \(\tan\frac{A}{2} = \frac{3}{2},\) then \(\frac{1 + \cos A}{1 - \cos A} =\)...

If tan⁡A2=32,\tan\frac{A}{2} = \frac{3}{2}, then 1+cos⁡A1−cos⁡A=\frac{1 + \cos A}{1 - \cos A} =

A

−5- 5

B

55

C

9/49/4

D

4/94/9

Answer

4/94/9

Explanation

Solution

Given that tan⁡A2=32\tan\frac{A}{2} = \frac{3}{2}.

1+cos⁡A1−cos⁡A=2cos⁡2A22sin⁡2A2=cot⁡2A2=(23)2=49\frac{1 + \cos A}{1 - \cos A} = \frac{2\cos^{2}\frac{A}{2}}{2\sin^{2}\frac{A}{2}} = \cot^{2}\frac{A}{2} = \left( \frac{2}{3} \right)^{2} = \frac{4}{9}.