Question

If 2 sin θ = x and x sec θ = 2 then find the value of 2tanθ + 1?
1. 1
2. 4
3. 3
4. √2

Answer 1

Correct Answer - Option 3 : 3

Given:

It is given that 2 sin θ = x and x sec θ = 2

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

tanθ = sinθ/cosθ

secθ = 1/cosθ

Calculation:

2sinθ = x

∴ sinθ = x/2

And x secθ = 2

∴ Secθ = 2/x

⇒ cosθ = x/2

Now, we have to find the value of 2tanθ + 1 = 2(sinθ/cosθ) + 1

Put the value of sin θ and cos θ in the given expression

∴ 2[(x/2)/(x/2)] + 1 = 2 + 1 = 3

Hence, option (3) is correct