How do you verify the identity $sqrt((1+sintheta)/(1-sintheta))=(1+sintheta)/abscostheta$ ?

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Answer 1 · 2017-01-17T18:48:05

see below

Left Hand Side:

$sqrt ((1+sin theta)/(1-sin theta))=sqrt ((1+sin theta)/(1-sin theta) *((1+sin theta)/(1+sin theta))$

$=sqrt ((1+sin theta)^2/(1-sin ^2theta))$

$=sqrt ((1+sin theta)^2/(cos ^2theta))$

$=sqrt ((1+sin theta)^2) / sqrt (cos^2 theta)$

$=(1+sin theta)/abs( cos theta)$ since $sqrt(x^2) = abs(x)$

$:.=$ Right Hand Side

How do you verify the identity sqrt((1+sintheta)/(1-sintheta))=(1+sintheta)/abscosthetasqrt((1+sintheta)/(1-sintheta))=(1+sintheta)/abscostheta?