Question

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Find the general solution of the given equation

$\cos {}^{2} x \: cosec \: x \: + 3sin \: x + 3 = 0$
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Answer 1

$\large{\mathbf{HELLO \: \: DEAR,}}$

$\mathit{cos^2x*cosecx + 3sinx + 3 = 0}\\ \\ \mathit{(1 - sin^2x)*cosecx + 3(sinx + 1) = 0} \\ \\ \mathit{(1 - sinx)(1 + sinx)*\frac{1}{sinx} + 3(sinx + 1) = 0} \\ \\ \mathit{(1 + sinx)[(1 - sinx)\frac{1}{sinx} + 3)] = 0}\\ \\ \mathit{(1 + sinx)(cosecx - 1 + 3) = 0}\\ \\ \mathit{(1 + sinx)(cosecx + 2) = 0}\\ \\ \mathit{(1 + sinx) = 0}\\ \\\mathit{sinx = - sin\frac{\pi}{2}}\\ \\ \mathit{sinx = sin(\frac{\pi}{2} + \pi)}\\ \\ \mathit{sinx = sin\frac{3\pi}{2}} \\ \\ \mathit{x = n\pi + (-1)^n \frac{3\pi}{2}}$

$\mathbf{sin 2x = -\frac{1}{2}}\\ \\\mathbf{sin x=- sin\frac{\pi}{6}} \\ \\ \mathbf{sinx = sin(\pi + \frac{\pi}{6})}\\ \\ \mathbf{sinx = sin\frac{7\pi}{6}} \\ \\ \mathbf{x = n\pi + (- 1)^n\frac{7\pi}{6}}\\ \\ \mathbf{x = {n\pi} + (-1)^n\frac{7\pi}{6}}$

$\large{\mathbf{\underline{I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}}}$

Answer 2

hope this helps you..