How do you simplify $cot x (sin x - csc x)$ $cotx (sinx-cscx)$ ?

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How do you simplify $cot x (sin x - csc x)$ $cotx (sinx-cscx)$ ?

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Answer 1 · 2018-05-07T15:41:04

The answer
$\frac{- cos x ({cos}^{2} x)}{{sin}^{2} x} = - cos x \cdot {cot}^{2} x$ $[-cosx(cos^2x)]/sin^2x=-cosx*cot^2x$

Explanation:

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$cot x (sin x - csc x)$ $cotx (sinx-cscx)$

$cot x \cdot sin x - cot x \cdot csc x$ $cotx*sinx-cotx*cscx$

$cot x = \frac{cos x}{sin x}$ $cotx=cosx/sinx$

$csc x = \frac{1}{sin x}$ $cscx=1/sinx$

$\frac{cos x}{sin x} \cdot sin x - \frac{cos x}{sin x} \cdot \frac{1}{sin x}$ $cosx/sinx*sinx-cosx/sinx*1/sinx$

$cos x - \frac{cos x}{{sin}^{2} x} = \frac{cos x \cdot {sin}^{2} x - cos x}{{sin}^{2} x} = \frac{- cos x (1 - {sin}^{2} x)}{{sin}^{2} x}$ $cosx-cosx/sin^2x=[cosx*sin^2x-cosx]/sin^2x=[-cosx(1-sin^2x)]/sin^2x$

$1 - {sin}^{2} x = {cos}^{2} x$ $1-sin^2x=cos^2x$

$\frac{- cos x ({cos}^{2} x)}{{sin}^{2} x} = - cos x \cdot {cot}^{2} x$ $[-cosx(cos^2x)]/sin^2x=-cosx*cot^2x$

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How do you simplify $cot x (sin x - csc x)$ $cotx (sinx-cscx)$ ?

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