Question

If cos θ = 1/2 and p = tan θ then find the value of p² – 5p – 2.
1. 1 - 5√3
2. 2 - 3√3
3. 7√3
4. 7 + √2
5. 3 + √3

Answer 1

Correct Answer - Option 1 : 1 - 5√3

Given:

cos θ = 1/2 and p = tan θ

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

Cos 60° = 1/2 and tan 60° = √3

Calculation:

We know that Cos 60° = 1/2

∴ Cos θ = Cos 60°

⇒ θ = 60°

Now, p = tan θ

∴ p = tan θ = tan 60° = √3

⇒ p = √3

Now, put the value of p in the given equation p² – 5p – 2

∴ (√3)² – 5(√3) – 2 = 1 - 5√3

Hence, option (1) is correct