Question

Prove that

√(1+sin∅)/(1-sin∅) = tan∅+sec∅

Answer 1

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Answer : Refer Attached Image
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Answer 2

here I am writing this symbol ∅ as a. Since It is difficult for me to write always.

Given RHS is tan a + Seca.

On squaring, we get

(Seca + tana)^2

sec^2a + tan^2a + 2secatana

$\frac{1}{ cos^{2}a } + \frac{sina}{cosa} + 2 * \frac{1}{cosa} * \frac{sina}{cosa}$

$\frac{1 + 2sina+ sin^{2}a }{ cos^{2}a }$

$\frac{(1+sina)(1+sina)}{1- sin^{2}a }$

$\frac{(1+sina)(1+sina)}{(1+sina)(1-sina)}$

$\frac{1+sina}{1-sina}$


Therefore,

$(seca+tana) = \sqrt{ \frac{1+sina}{1-sina} }$


Hope this helps!