If tan Θ + cot Θ = 4

Find the ratio of 3(tan² Θ + cot² Θ) to (2cosec² Θ sec² Θ - 4)

3 : 2

tan (Θ) + cot Θ = 4

cot (90 - Θ) + cot Θ = 4

2cot Θ = 4

cot Θ  = \(\frac{b}{P}\) = \(\frac{2}{1}\)

       H = \(\sqrt {5}\)

⇒3(tan² Θ + cot² Θ) : (2cosec² Θ sec² Θ - 4) = \(\frac{3 × (\frac{1}{4} + 4)}{(2 × \frac{5}{1} × \frac{5}{4} - 4)}\)

= \(\frac{\frac{51}{4}}{\frac{25}{2} - 4}\) = \(\frac{51}{4}\) × \(\frac{2}{17}\) = 6 : 4 = 3 : 2