Question

plz answer this ques
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Answer 1

Answer:

Take lcm

$\frac{ \sqrt{ \sec(x) - 1 } }{\sqrt{ \sec(x) + 1 } } + \frac{ \sqrt{ \sec(x) + 1 } }{\sqrt{ \sec(x) - 1 } } \\ \\ = \frac{ (\sqrt{ \sec(x) - 1 }) {}^{2} + ( \sqrt{ \sec(x) + 1 }) {}^{2} }{\sqrt{ \sec(x) - 1 } \sqrt{ \sec(x) + 1 } } \\ \\ square \: \: and \: \: roots \: cancels \: each \: out\\ \\ = \frac{ \sec(x) - 1 + \sec(x) + 1 }{ \sqrt{ \sec {}^{2} (x) - 1 } } \\ \\ = \frac{2 \sec(x) }{ \sqrt{ \tan {}^{2} (x) } } \\ \\ = \frac{2 \sec(x) }{ \tan(x) } \\ \\ = \frac{ \frac{2}{ \cos(x) } }{ \frac{ \sin(x) }{ \cos(x) } } \\ \\ = \frac{2}{ \sin(x) } \\ \\ = 2 \cosec(x) \\ \\ = rhs$