Question

If cot ????=1/√3, show that 1-cos²????/2-sin²????=3/5

Answer 1

1 - cos²θ / 2 - sin²θ = 3/5  proved

Step-by-step explanation:

Given:  

cot θ = 1/√3

We know that Cot 60° = 1/√3

So we find that θ = 60°  

Now to show that 1 - cos²θ / 2 - sin²θ = 3/5

Proof:

LHS = 1-cos²θ / 2-sin²θ  

    = Sin²θ / 1 + Cos²θ

    = Sin²60° / 1 + Cos²60°

    = (√3/2)² / 1+ (1/2)²

    = 3/4 / 1+1/4

    = 3/4 / 5/4

    = 3/5

 LHS = RHS

Hence proved.