Solution
Review all six trigonometric ratios: sine, cosine, tangent, cotangent, secant, & cosecant
Given,
$cot θ = 1/√3$
Using $cosec2 θ − cot2 θ = 1$,we can find cosec θ
$cosec θ = √(1 + cot2 θ)$
$= √(1 + (1/√3)2)$
$= √(1 + (1/3)) = √((3 + 1)/3)$
$= √(4/3)$
⇒ $cosec θ = 2/√3$
So, $sin θ = 1/ cosec θ = 1/ (2/√3)$
⇒ $sin θ = √3/2$
And, we know that
$cos θ = √(1 – sin2 θ)$
$= √(1 – (√3/2)2)$
$= √(1 – (3/4))$
$= √((4 – 3)/4)$
$= √(1/4)$
⇒ $cos θ = ½$
Now, using cos θ and sin θ in the expression, we have
$= 3/5$