Question

Solve the following trig equation and state the solutions: 2sinx-cscx=0

Answer 1

ANSWER ON QUESTION #54780 – Math – Trigonometry

Solve the following trig equation and state the solutions: $2\sin x - csc x = 0$

Solution

Since $\csc x = \frac{1}{\sin x} (x \neq \pi k, k \in \mathbb{Z})$, then

the equation $2\sin x - csc x = 0$ is equivalent to the following equation

$$2 \sin x - \frac{1}{\sin x} = 0$$

We have

$$\sin^2 x = \frac{1}{2}$$ $$\sin x = \pm \frac{1}{\sqrt{2}}$$ $$x = \frac{\pi}{4} + \pi k, \quad k \in \mathbb{Z}$$

Answer: $x = \frac{\pi}{4} + \pi k$, $k \in \mathbb{Z}$.

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