How do you prove $csc x - sin x = cos x cot x$ $csc x - sin x = cos x cot x$ ?

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How do you prove $csc x - sin x = cos x cot x$ $csc x - sin x = cos x cot x$ ?

2 Answers

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Answer 1 · 2018-06-07T07:37:55

see below

Explanation:

$csc x - sin x$ $cscx-sinx$

$= \frac{1}{sin x} - sin x$ $=1/sinx-sinx$

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

$= \frac{{cos}^{2} x}{sin x}$ $=cos^2x/sinx$

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

$= cos x cot x$ $=cosxcotx$

Answer 2 · 2018-06-07T07:38:27

Please see the proof below

Explanation:

We need

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

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

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

Therefore,

$L H S = csc x - sin x$ $LHS=cscx-sinx$

$= \frac{1}{sin x} - sin x$ $=1/sinx-sinx$

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

$= \frac{{cos}^{2} x}{sin x}$ $=cos^2x/sinx$

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

$= cos x cot x$ $=cosxcotx$

$= R H S$ $=RHS$

$Q E D$ $QED$

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How do you prove $csc x - sin x = cos x cot x$ $csc x - sin x = cos x cot x$ ?

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Explanation:

Explanation:

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