How to solve this identity? Thank you!

Question

How to solve this identity? Thank you!

You need to prove that $cot x - cot y = \frac{sin (y - x)}{sin x \cdot sin y}$ $cotx - coty = (sin(y-x))/(sinx * siny)$

Thank you very much!

1 Answer

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Answer 1 · 2017-12-08T19:55:28

$see explanation$ $"see explanation"$

Explanation:

$using the trigonometric identities$ $"using the "color(blue)"trigonometric identities"$

$∙ x sin (y - x) = sin y cos x - cos y sin x$ $•color(white)(x)sin(y-x)=sinycosx-cosysinx$

$∙ x cot x = \frac{cos x}{sin x}$ $•color(white)(x)cotx=cosx/sinx$

$consider the left side$ $"consider the left side"$

$cot x - cot y$ $cotx-coty$

$= \frac{cos x}{sin x} - \frac{cos y}{sin y}$ $=cosx/sinx-cosy/siny$

$= \frac{cos x sin y - sin x cos y}{sin x sin y}$ $=(cosxsiny-sinxcosy)/(sinxsiny)$

$= \frac{sin (y - x)}{sin x sin y}$ $=(sin(y-x))/(sinxsiny)$

$= right side \Rightarrow verified$ $=" right side "rArr" verified"$

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Math

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How to solve this identity? Thank you!

You need to prove that $cot x - cot y = \frac{sin (y - x)}{sin x \cdot sin y}$ $cotx - coty = (sin(y-x))/(sinx * siny)$

Thank you very much!

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How to solve this identity? Thank you!

You need to prove that cotx−coty=sin(y−x)sinx⋅sinycotx - coty = (sin(y-x))/(sinx * siny) Thank you very much!

1 Answer

Explanation:

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Impact of this question

You need to prove that $cot x - cot y = \frac{sin (y - x)}{sin x \cdot sin y}$ $cotx - coty = (sin(y-x))/(sinx * siny)$

Thank you very much!