Question

Prove that cotA/(cosec A+1)+(cosecA+1)/cotA=2secA

Answer 1

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Answer 2

$\frac{cota}{coseca + 1} + \frac{coseca + 1}{cota} \\ \\ = \frac{ {cot}^{2}a + ( {coseca + 1)}^{2} }{cota(coseca + 1)} \\ \\ = \frac{ {cot}^{2} a + {cosec}^{2}a + 1 + 2coseca }{cota(coseca + 1)} \\ \\ = \frac{2 {cosec}^{2}a + 2coseca }{cota(coseca + 1)} \\ \\ = \frac{2coseca}{cota} \\ \\ = 2 \frac{1}{sina} \frac{sina}{cosa} \\ \\ = 2seca$