Question

If \(\cos x=\frac{-1}{2}\) and \(\pi<x<\frac{3\pi}{2}\), find the value of 4 tan²x - 3 cosec²x.
1. 16
2. 10
3. 12
4. 8

Answer 1

Correct Answer - Option 4 : 8

Given:

\(\cos x=\frac{-1}{2}\) where \(π<x<\frac{3π}{2}\) 

Formula used:

cos(π + x) = - cos x    ∵ [\(π<x<\frac{3π}{2}\)]

Calculation:

cos x = - 1/2 

⇒ cos x = cos(π + π/3) 

⇒ x = 4π/3 

4 tan2x - 3 cosec2x 

⇒ 4 × (√3)² - 3 × (- 2/√3)²

⇒ 4 × 3 - 3 × 4/3 

⇒ 12 - 4 

⇒ 8 

∴ The required value is 8.

The value of tan and cot is positive in the third quadrant.