If , where , then find the possible values of…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

If cos⁡5α=cos⁡5α\cos 5\alpha = \cos^5 \alpha , where α∈(0,π2)\alpha \in \left( 0, \frac{\pi}{2} \right) , then find the possible values of (sec⁡2α+csc⁡2α+cot⁡2α)(\sec^2 \alpha + \csc^2 \alpha + \cot^2 \alpha) .

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