How do you rationalize the numerator for $\sqrt{\frac{1 + sin y}{1 - sin y}}$ $sqrt((1+siny)/(1-siny))$ ?

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How do you rationalize the numerator for $\sqrt{\frac{1 + sin y}{1 - sin y}}$ $sqrt((1+siny)/(1-siny))$ ?

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Answer 1 · 2016-09-03T14:42:12

The expression can be simplified to $\frac{1 + sin y}{cos y}$ $(1 + siny)/cosy$ .

Explanation:

$\frac{\sqrt{1 + sin y}}{\sqrt{1 - sin y}}$ $sqrt(1 + siny)/sqrt(1 - siny)$

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

$= \frac{\sqrt{1 + sin y}}{\sqrt{1 - sin y}} \times \frac{\sqrt{1 + sin y}}{\sqrt{1 + sin y}}$ $=sqrt(1 + siny)/sqrt(1 - siny) xx sqrt(1 + siny)/sqrt(1 + siny)$

$= \frac{1 + sin y}{\sqrt{1 - {sin}^{2} y}}$ $=(1 + siny)/sqrt(1 - sin^2y)$

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

$= \frac{1 + sin y}{\sqrt{{cos}^{2} y}}$ $=(1 + siny)/(sqrt(cos^2y)$

$= \frac{1 + sin y}{\sqrt{cos y \times cos y}}$ $=(1 + siny)/(sqrt(cosy xx cosy))$

$= \frac{1 + sin y}{cos y}$ $=(1 + siny)/cosy$

Hopefully this helps!

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How do you rationalize the numerator for $\sqrt{\frac{1 + sin y}{1 - sin y}}$ $sqrt((1+siny)/(1-siny))$ ?

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How do you rationalize the numerator for $\sqrt{\frac{1 + sin y}{1 - sin y}}$ $sqrt((1+siny)/(1-siny))$ ?