Question

Prove that under root 1+sin upon 1-sin + under root 1-sin upon 1+sin = 2sec

Answer 1

Hlew,

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Sorry baby 'wink'

Answer 2

Answer:

$lhs \\ = \sqrt \frac{ 1+ \sin }{1 - \sin} + \sqrt \frac{ 1 - \sin }{1 + \sin} \\ = \sqrt \frac{(1 + \sin)(1 + \sin) }{(1 - \sin)(1 + \sin) } + \sqrt \frac{(1 - \sin)(1 - \sin) }{(1 + \sin)(1 - \sin) } \\ = \sqrt \frac{ {(1 + \sin) }^{2} }{1 - { \sin }^{2} } + \sqrt \frac{ {(1 - \sin) }^{2} }{1 - { \sin }^{2} } \\ = \sqrt \frac{ {(1 + \sin) }^{2} }{ { \cos }^{2} } +\sqrt \frac{ {(1 - \sin) }^{2} }{ { \cos }^{2} }\\ = \frac{1 + \sin }{ \cos} + \frac{1 - \sin }{ \cos}\\ = \frac{1}{ \cos } + \frac{ \sin }{ \cos } + \frac{1}{ \cos } - \frac{ \sin }{ \cos } \\ = \frac{2}{ \cos} \\ = 2 \sec \\ = rhs$

Hence, proved