The Whimsical Cosine

Geometry Level 5

∑r=110sec⁡4rθ=88+acos⁡4θ\sum_{r=1}^{10} \sec^{4r} \theta=88+\frac {a}{\cos^4 \theta}

Given cos⁡8θ+cos⁡4θ=1.\cos^8 \theta+\cos^4 \theta=1. and that it satisfy the equation above for some constant aa. Find aa.

Note: This is one of my original problems. It belongs to the set- Questions I've Made ©.
Sanjeet Raria by Sanjeet Raria
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