Mathematics: Find all exact solutions on [0, 2π). (Enter your answers as a comma-separated list.) tan(x) − 2 sin(x) tan(x) = 0.

The surface area is 33ft square....

Find all exact solutions on [0, 2π). (Enter your

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11.02.2022

$0, \dfrac{\pi}{6}, \dfrac{5\pi}{6}, \pi$

Step-by-step explanation:

Given the equation:

sin(x)-2sin(x) tan(x)=0

To find:

The solutions of given equation in the range [0, 2 $\pi$ ) i.e. 0 can be in the answer but $2\pi$ can not be there in the answer.

Solution:

Taking tan(x) common, we get:

tan(x) (1-2sin(x))=0

The solutions can be given as:

tan(x) = 0 OR 1-2sin(x) = 0

Let us solve both the equations one by one:

First equation:

$tan(x) = 0\\ \Rightarrow x=0, \pi$

Second equation:

$1-2sin(x) = 0\\\Rightarrow 2sinx=1\\\Rightarrow sinx=\dfrac{1}{2}\\\Rightarrow x = \dfrac{\pi}{6}, \dfrac{5\pi}{6}$

Therefore, the answers as a comma separated list are:

$0, \dfrac{\pi}{6}, \dfrac{5\pi}{6}, \pi$

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