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If ${cosec}^{6} θ - \cot^{6} θ = a \cot^{4} θ + b \cot^{2} θ + c$ then $a + b + c =$

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answer is B.

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Detailed Solution

${cosec}^{6} θ - \cot^{6} θ = a \cot^{4} θ + b \cot^{2} θ + c$

$\begin{array}{rcl} \cot θ & = & 1 \Rightarrow θ = \frac{π}{4} \\ a + b + c & = & {cosec}^{6} \frac{π}{4} - \cot^{6} \frac{π}{4} \\ = & 2^{3} - 1 \\ = & 7 \end{array}$

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