# What's equivalent to = cos theta/1 - sin^2 theta?

## note that the answer must be one of these choices: a) cos theta b) csc thata c) tan theta d) sec theta

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1
Nov 19, 2017

d)

#### Explanation:

$\cos \frac{\theta}{1 - {\sin}^{2} \theta}$

${\sin}^{2} \theta + {\cos}^{2} \theta = 1$ (Identity )

$\therefore$ $1 - {\sin}^{2} \theta = {\cos}^{2} \theta$

$\cos \frac{\theta}{{\cos}^{2} \theta} = \frac{1}{\cos} \theta = \sec \theta$

$\sec \theta = \frac{1}{\cos} \theta$ (Identity)

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Jim G. Share
Nov 19, 2017

#### Answer:

$\sec \theta \to \left(d\right)$

#### Explanation:

$\text{using the "color(blue)"trigonometric identities}$

•color(white)(x)cos^2theta+sin^2theta=1

•color(white)(x)sectheta=1/costheta

$\Rightarrow \frac{\cos \theta}{1 - {\sin}^{2} \theta}$

$= \frac{\cos \theta}{{\cos}^{2} \theta}$

$= \frac{1}{\cos} \theta$

$= \sec \theta$

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