How would you prove or disprove $cotx - cosx/cotx = cos^2x/(1 + sinx)$ ?

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Answer 1 · 2016-10-30T03:25:32

Rewrite all terms in $cotx$ as $cosx/sinx$ .

$cosx/sinx - cosx/(cosx/sinx) = cos^2x/(1 + sinx)$

$cosx/sinx - cosx xx sinx/cosx = cos^2x/(1 + sinx)$

$cosx/sinx - sinx = cos^2x/(1 + sinx)$

Rewrite the right-hand side using the identity $sin^2x + cos^2x = 1$ .

$cosx/sinx - sinx = (1 - sin^2x)/(1 + sinx)$

$cosx/sinx - sinx = ((1 + sinx)(1 - sinx))/(1 + sinx)$

$cosx/sinx - sinx = 1 - sinx$

$(cosx - sin^2x)/sinx = 1 - sinx$

The identity is false, because no matter what you do with the left hand side, you will never be able to get on the right.

Hopefully this helps!

How would you prove or disprove cotx - cosx/cotx = cos^2x/(1 + sinx)cotx - cosx/cotx = cos^2x/(1 + sinx)?