Question

`2 \sin(x) - √(3) = 0`


`when(\pi)/(2) \leqslant x \leqslant \pi`
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Answer 1

Given:

The equation is

`2\sin x-√(3)=0`

When
`(\pi)/(2)\leq x\leq \pi`.

To find:

The value of x.

Solution:

We have,

`2\sin x-√(3)=0`

It can be written as

`2\sin x=√(3)`

`\sin x=(√(3))/(2)`

It is given that
`(\pi)/(2)\leq x\leq \pi`.

`\sin x=\sin \left(\pi-(\pi)/(3)\right)`

`x=(3\pi-\pi)/(3)`

`x=(2\pi)/(3)`

Therefore, the value of x is
`(2\pi)/(3)`.