How do you rationalize the numerator for $sqrt((1+siny)/(1-siny))$ ?

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Answer 1 · 2016-09-03T14:42:12

The expression can be simplified to $(1 + siny)/cosy$ .

$sqrt(1 + siny)/sqrt(1 - siny)$

Multiply by the entire expression by the numerator to cancel the square root:

$=sqrt(1 + siny)/sqrt(1 - siny) xx sqrt(1 + siny)/sqrt(1 + siny)$

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

This can be simplified further. Apply the pythagorean identity $1 - sin^2theta = cos^2theta$ .

$=(1 + siny)/(sqrt(cos^2y)$

$=(1 + siny)/(sqrt(cosy xx cosy))$

$=(1 + siny)/cosy$

Hopefully this helps!

How do you rationalize the numerator for sqrt((1+siny)/(1-siny))sqrt((1+siny)/(1-siny))?