Question

Sin inverse 1 by root 5 + Cos inverse X is equal to 1. find x?

Answer 1

`x~~0.8595783384`

Explanation:

Given
`color(white)("XXX")arcsin(1/sqrt(5))+arccos(x)=1`

`color(white)("XXX")rarr arccos(x)=1-arcsin(1/sqrt(5))`

Note: I have assumed angles are in Quadrant I

Using a calculator (or spreadsheet function)
`color(white)("XXX")arcsin(1/sqrt(5))~~0.463647609`

Therefore
`color(white)("XXX")arccos(x)~~1-0.463647609 =0.53352391`
and
`color(white)("XXX")cos(arccos(x))~~cos(0.53352391)`

`color(white)("XXX")rarr x~~cos(0.53352391)`

Then using a calculator or spreadsheet function again
`color(white)("XXX")x~~0.8595783384`