How do you prove this identity?

Question

How do you prove this identity?

Prove:

$cot x = sin x sin (\frac{π}{2} - x) + {cos}^{2} x cot x$ $cotx=sinxsin(pi/2-x)+cos^2xcotx$

Please and thanks :)

1 Answer

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Answer 1 · 2017-11-26T00:13:14

See below.

Explanation:

These are the identities I use in this proof:

$sin (\frac{π}{2} - x) = cos x$ $sin(pi/2 - x) = cos x$

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

$x$ $color(white)x$

$cot x = sin x sin (\frac{π}{2} - x) + {cos}^{2} x cot x$ $cot x = sin x sin (pi/2 - x) + cos^2 x cot x$

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

$= sin x cos x + ({cos}^{2} x \cdot \frac{cos x}{sin x})$ $=sin x cos x + (cos^2 x * cos x / sin x)$

$= sin x cos x + \frac{{cos}^{3} x}{sin x}$ $=sin x cos x + cos^3x/sin x$

$= \frac{{sin}^{2} x cos x}{sin x} + \frac{{cos}^{3} x}{sin x}$ $=(sin^2 x cos x) / sin x + cos^3x/sin x$

$= \frac{{sin}^{2} x cos x + {cos}^{3} x}{sin x}$ $=(sin^2 x cos x + cos ^3x )/sin x$

$= \frac{cos x ({sin}^{2} x + {cos}^{2} x)}{sin x}$ $=(cos x (sin^2x + cos^2x))/sin x$

$= \frac{cos x \cdot 1}{sin x}$ $=(cos x *1) /sin x$

$= \frac{cos x}{sin x}$ $=cos x / sin x$

$= cot x$ $=cot x$

$x cot x = cot x$ $color(white)x cot x = cot x$

Science

Math

Humanities

... and beyond

How do you prove this identity?

Prove:

$cot x = sin x sin (\frac{π}{2} - x) + {cos}^{2} x cot x$ $cotx=sinxsin(pi/2-x)+cos^2xcotx$

Please and thanks :)

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you prove this identity?

Prove: cotx=sinxsin(π2−x)+cos2xcotxcotx=sinxsin(pi/2-x)+cos^2xcotx Please and thanks :)

1 Answer

Explanation:

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Impact of this question

Prove:

$cot x = sin x sin (\frac{π}{2} - x) + {cos}^{2} x cot x$ $cotx=sinxsin(pi/2-x)+cos^2xcotx$

Please and thanks :)