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Question Number 85484 by oustmuchiya@gmail.com last updated on 22/Mar/20

$$showthat\frac{1}{sec\theta +1}+\frac{1}{sec\theta -1}\equiv 2cosec\theta cot\theta$$

Answered by som(math1967) last updated on 18/Apr/20

$$\frac{\sec \theta -1+sec\theta +1}{(sec\theta +1)(sec\theta -1)}$$$$=\frac{2sec\theta }{{sec}^2\theta -1}=\frac{2sec\theta }{{tan}^2\theta }=\frac{2sec\theta {cos}^2\theta }{{sin}^2\theta }$$$$=\frac{2cos\theta }{sin\theta .sin\theta }=2cosec\theta cot\theta$$

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