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.