Question

How do you find a numerical value of one trigonometric function of x given `cscx/cotx=sqrt2`?

Answer 1

`:.x=+-pi/4+2pin`

Explanation:

`cscx/cotx=sqrt2`

`(1/sinx)/(cosx/sinx)=sqrt2`

`1/sinx * sinx/cosx=sqrt2`

`1/cancelsinx * cancelsinx/cosx=sqrt2`

`1/cosx=sqrt2`

`1=sqrt2 cosx`

`1/sqrt2 =cosx`

`cos^-1 (1/sqrt2) =x`

`:.x=+-pi/4+2pin`