How do you simplify $(1 - {cos}^{2} x) (csc x)$ $(1-cos^2x)(cscx)$ ?

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How do you simplify $(1 - {cos}^{2} x) (csc x)$ $(1-cos^2x)(cscx)$ ?

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Answer 1 · 2017-02-10T00:43:39

This simplifies to $sin x$ $sinx$ .

Explanation:

Use ${sin}^{2} θ + {cos}^{2} θ = 1 \to {sin}^{2} θ = 1 - {cos}^{2} θ$ $sin^2theta + cos^2theta = 1 -> sin^2theta = 1- cos^2theta$ and $csc θ = \frac{1}{sin θ}$ $csctheta = 1/sintheta$ .

$= ({sin}^{2} x) (csc x)$ $=(sin^2x)(cscx)$

$= ({sin}^{2} x) (\frac{1}{sin x})$ $= (sin^2x)(1/sinx)$

$= sin x$ $= sinx$

Hopefully this helps!

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How do you simplify $(1 - {cos}^{2} x) (csc x)$ $(1-cos^2x)(cscx)$ ?

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Explanation:

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How do you simplify $(1 - {cos}^{2} x) (csc x)$ $(1-cos^2x)(cscx)$ ?