If (sin²θ)/(tan²θ-sin²θ)=5 , θ is an acute angle, then the value of (24sin²θ-15sec²θ)/(6cosec²θ-7cot²θ) is:

If (sin²θ)/(tan²θ-sin²θ)=5 , θ is an acute angle, then the…

If $\dfrac{sin^2\theta}{tan^2\theta-sin^2\theta}=5$ , θ is an acute angle, then the value of $\dfrac{24sin^2\theta-15sec^2\theta}{6cosec^2\theta-7cot^2\theta}$ is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. -14

⇒ sin² $\theta$ /(tan² $\theta$ - sin² $\theta$ ) = 5

⇒ sin² $\theta$ × cos² $\theta$ /(sin² $\theta$ (1 - cos² $\theta$ )) = 5

⇒ cot² $\theta$ = 5

cot $\theta$ = $\sqrt5$ = b/p

By using pythagoras theorem,

H² = 5 + 1

H = $\sqrt6$

⇒ (24 × 1/6 - 15 × 6/5)/(6 × 6 - 7 × 5)

⇒ (4 - 18)/(1)

= -14.

SSC CGL 2021 PYQ — Question 72