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

s h o w t h a t \frac{1}{s e c θ + 1} + \frac{1}{s e c θ - 1} \equiv 2 c o s e c θ c o t θ

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

\frac{\sec θ - 1 + s e c θ + 1}{(s e c θ + 1) (s e c θ - 1)}

= \frac{2 s e c θ}{{s e c}^{2} θ - 1} = \frac{2 s e c θ}{{t a n}^{2} θ} = \frac{2 s e c θ {c o s}^{2} θ}{{s i n}^{2} θ}

= \frac{2 c o s θ}{s i n θ . s i n θ} = 2 c o s e c θ c o t θ