If tan θ = √(5) , then the value of (cosec² θ + sec² θ)/(cosec² θ - sec² θ) is:

If tan θ = √(5) , then the value of (cosec² θ + sec²…

If tan $\theta$ = $\sqrt{5}$ , then the value of $\frac{cosec^2 \theta + sec^2 \theta}{cosec^2 \theta - sec^2 \theta}$ is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. $-\frac{3}{2}$ .

tan $\theta$ = $\sqrt{5}$ = P/B

H² = $\sqrt{5}$ ² + 1²

H = $\sqrt{6}$

⇒ $\frac{cosec^2 \theta + sec^2 \theta}{cosec^2 \theta - sec^2 \theta}$

⇒ $\frac{(\sqrt{\frac65}^2 + \sqrt6^2)}{(\sqrt{\frac65}^2 - \sqrt6^2)}$

⇒ $\frac{\frac{36}{5}}{\frac{-24}{5}}$ = $-\frac{3}{2}$ .