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Question: If \(90^{o} < A < 180^{o}\) and \(\sin A = \frac{4}{5},\) then\(\tan A/2\) is equal to...

If 90o<A<180o90^{o} < A < 180^{o} and sin⁡A=45,\sin A = \frac{4}{5}, thentan⁡A/2\tan A/2 is equal to

A

12\frac{1}{2}

B

35\frac{3}{5}

C

32\frac{3}{2}

D

2

Answer

2

Explanation

Solution

sin⁡A=45⇒tan⁡A=−43\sin A = \frac{4}{5} \Rightarrow \tan A = - \frac{4}{3}, (90o<A<180o)(90^{o} < A < 180^{o})

tan⁡A=2tan⁡A/21−tan⁡2A/2,\tan A = \frac{2\tan A/2}{1 - \tan^{2}A/2}, Lettan⁡A2=P\tan\frac{A}{2} = P

⇒\Rightarrow −43=2P1−P2\frac{- 4}{3} = \frac{2P}{1 - P^{2}} ⇒ 4P2−6P−4=04P^{2} - 6P - 4 = 0⇒P=−12P = - \frac{1}{2}, 2

⇒ P=−12P = - \frac{1}{2} (impossible)

So, P=2P = 2 i.e., tan⁡A/2=2.\tan A/2 = 2.