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Question
Prove the following:
cos 36° = `(sqrt(5) + 1)/4`
Solution
We know that,
cos 2θ = 1 – 2sin2θ
cos 36° = cos 2(18°) = 1 – 2 sin218°
= `1 - 2((sqrt(5) - 1)/4)^2`
= `(8 - (5 + 1 - 2sqrt(5)))/8`
= `(8 - (6 - 2sqrt(5)))/8`
= `(2 + 2sqrt(5))/8`
∴ cos 36° = `(sqrt(5) + 1)/4`
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