Question

If cos θ = `- sqrt(3)/2` and sin α = `-3/5`, where θ does not and α lies in the third quadrant, then `(2 tan α + sqrt(3) tan θ)/(cot^2 θ + cos alpha)` is equal to ______.

विकल्प

• `7/22`

• `5/22`

• `9/22`

• `22/5`

Answer 1

If cos θ = `- sqrt(3)/2` and sin α = `-3/5`, where θ does not and α lies in the third quadrant, then `(2 tan α + sqrt(3) tan θ)/(cot^2 θ + cos alpha)` is equal to `underlinebb(5/22)`.

Explanation:

Given, cos θ = `-sqrt(3)/2 < 0` and θ does not lie in III quadrant.

∴ θ must be lying in II quadrant.

`\implies` tan θ = `-1/sqrt(3)` and cot θ = `-sqrt(3)`  ...(i)

Since, α lies in III quadrant and sin α = `-3/5`

∴ tan α = `3/4` and cos α = `-4/5`  ...(ii)

Now, `(2tanα + sqrt(3) tan θ)/(cot^2θ + cos α)`

= `(2. 3/4 - sqrt(3). 1/sqrt(3))/(3 - 4/5)`

= `5/22`