If tan Θ + cot Θ = 4
Find the ratio of 3(tan2 Θ + cot2 Θ) to (2cosec2 Θ sec2 Θ - 4)
Answer & explanation
Correct answer: option 1
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