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General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2

The number of...

Question

The number of solutions of the equation $sin 2 x + 2 sin x - cos x - 1 = 0$ in the range $0 \leq x \leq 2 π$ is

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Solution

$\begin{matrix} sin x + 2 sin x - cos x - 1 2 sin x cos x + 2 sin x - cos - 1 2 sin x (cos x + 1) - (cos x + 1) cos x = - 1 sin x = \frac{1}{2} x = π + 2 n + 1, \frac{+ 1}{6}, \frac{5 π}{6} \end{matrix}$

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The number of solution of the equation $s i n x + s i n 2 x + s i n 3 x = c o s x + c o s 2 x + c o s 3 x, 0 \leq x \leq 2 π$ is

x^{3} + x^{2} + 4 x + 2 sin x = 0

0 \leq x \leq 2 π

x^{3} + x^{2} + 3 x + 2 s i n x = 0

- 2 π \leq x \leq 4 π

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

x \in [0, π]

sin 2 x + 2 sin x + 2 cos x + 1 = 0

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