Question

If `tanx=sqrt2`, then find `sinx` and `cosx`?

Answer 1

Either `sinx=sqrt(2/3)` and `cosx=1/sqrt3`
or `sinx=-sqrt(2/3)` and `cosx=-1/sqrt3`

Explanation:

As `tanx=sqrt2`

`secx=+-sqrt(1+(sqrt2)^2)=+-sqrt3`

and hence `cosx=+-1/sqrt3`

`sinx=tanxcosx=sqrt2xx(+-1/sqrt3)=+-sqrt(2/3)`

but as `tanx` is positive, `sinx` and `cosx` would be positive and negative together.