Question

I f sin x: cos x: : √3 : 1, find sin x, cos x.

Answer 1

sinx : cosx  = √3 :1

sinx/cosx =√3/1

tanx=√3                                         [sin/cos=tan]

x=tan⁻¹(√3)
  =60°= π/3


So substituting x as 60° we get,

⇒sinx=sin(60°)=√3/2

⇒cosx=cos(60°)=1/2

Answer 2

If a:b::c:d then ad=bc
Given
Sin x :cos x:: root3:1
sin x=root3 * cos x
sin x/cosx =root 3
tan x = root 3
tan x = tan 60
Therefore
x=60 degrees