Question

Prove that ✓((1+sinA)/1-sinA)=secA+tanA​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

the actual question is

prove that

$\sqrt{ \frac{1 + \sin(a) }{1 - \sin(a) } } = \sec(a) - \tan(a)$

taking LHS

rationalize the denominator

$\sqrt{ \frac{1 + \sin(a) }{1 - \sin(a) } \times \frac{1 + \sin(a) }{1 + \sin(a) } } \\ = \sqrt{ \frac{ {(1 + \sin(a)) }^{2} }{ {1}^{2} - { \sin(a) }^{2} } } \\ = \frac{ \sqrt{ {(1 + \sin(a)) }^{2} } }{ \sqrt{1 - { \sin(a) }^{2} } } \\ = \frac{1 + \sin(a) }{ \sqrt{ { \cos(a) }^{2} } } \\ = \frac{1 + \sin(a) }{ \cos(a) } \\ = \frac{1}{ \cos(a) } + \frac{ \sin(a) }{ \cos(a) } \\ = \sec(a ) + \tan(a)$

LHS=RHS

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