If cosecθ+cotθ over cosecθ-cotθ=7 , then the value of 4sin²θ+5 over 4sin²θ-1 is:

If cosecθ+cotθ over cosecθ-cotθ=7 , then the value of…

If ${{cosec\theta+cot\theta} \over cosec\theta-cot\theta}=7$ , then the value of ${{4sin^2\theta+5} \over 4sin^2\theta-1}$ is:

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 9.

Given that

${{cosec\theta+cot\theta} \over cosec\theta-cot\theta}=7$

By Componendo Dividendo Rule

${{(cosec\theta+cot\theta)+(cosec\theta-cot\theta)} \over (cosec\theta-cot\theta) - (cosec\theta+cot\theta)}$ = $\frac{8}{6}$

cosecθ/cotθ = 4/3

cosθ = 3/4

sin²θ = 7/16

Put value in given equation

${{4sin^2\theta+5} \over 4sin^2\theta-1}$ = ${{4(7/16)+5} \over 4(7/16)-1}$ = 27/9 = 9