How do you solve $cot x sec x + cot x = 0$ $cotxsecx+cotx=0$ and find all general solutions?

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Answer 1 · 2016-10-03T03:22:52

Factor:

$\frac{cos x}{sin x} (\frac{1}{cos x}) + \frac{cos x}{sin x} = 0$ $cosx/sinx(1/cosx) + cosx/sinx= 0$

$\frac{1}{sin x} + \frac{cos x}{sin x} = 0$ $1/sinx + cosx/sinx = 0$

$\frac{1 + cos x}{sin x} = 0$ $(1 + cosx)/(sinx) = 0$

$1 + cos x = 0$ $1 + cosx = 0$

$cos x = - 1$ $cosx= -1$

$x = π + π n$ $x = pi + pin$ , n an integer.

However, this solution renders the equation undefined, so there is no real solution.

Hopefully this helps!

How do you solve cotxsecx+cotx=0cotxsecx+cotx=0cotxsecx+cotx=0 and find all general solutions?