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    If then what is the value of cosecθ ?
    Question

    If then what is the value of cosecθ ?

    A.

    13/12

    B.

    3/2

    C.

    11/12

    D.

    9/13

    Correct option is A

    Given: ​
    ​cosec⁡θ+cot⁡θ=32\cosec \theta + \cot \theta = \frac{3}{2} 
    Concept Used: 
    ​1+cot⁡2θ=cosec⁡2θ ⟹ cosec⁡2θ−cot⁡2θ=1 ⟹ (cosec⁡θ+cot⁡θ)(cosec⁡θ−cot⁡θ)=1 ⟹ cosec⁡θ+cot⁡θ=1cosec⁡θ−cot⁡θ1 + \cot^2 \theta = \cosec^2 \theta \\ \implies \cosec^2 \theta - \cot^2 \theta = 1 \\ \implies (\cosec\theta + \cot \theta) (\cosec\theta -\cot \theta) = 1 \\ \implies \cosec\theta + \cot \theta = \frac{1}{\cosec\theta -\cot \theta} 
    Solution:
    ​

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