Question

5arcsin(x)-2pi=2arcsin(x)-3pi

Answer 1

The value of
`x=-{(√(3) )/(2) }`

Explanation:

We have to find the value of (x) from the trigonometric equation.

⇒
`5arcsin(x)-2\pi =2arcsin(x)-3\pi`

Subtracting
`2arcsin(x)` and adding
`2\pi` from both sides.

⇒
`3arcsin(x)=-\pi`

Dividing both sides with 3.

⇒
`arcsin(x)=(-\pi)/(3)`

Using arcsin(x)=a then x=sin(a) and
`sin(\pi)/(3) =(√(3) )/(2)`

So,

⇒
`x=sin(\frac{-\pi} {3}) =-(√(3) )/(2)`

Our final value of (x) =
`-(√(3) )/(2)`