Question

Cos²18°. Sin²36° - cos36°. Sin18°=?

Answer 1

Answer:

We have:

[math]cos(20) = cos^2(0)-sin^2(0) = 1-sin^2(0) sin^2(0) = [/math]

[math]1-2sin^2(0) ... (1)[/math]

Hence, by [math](1)[/math] we take:

[math]cos^2(36)+sin^2(18) = cos^2[2(18)]+sin^2(18) = [/math]

[math][1-2sin^2(18)]^2+sin^2(18) = 4sin^4(18)+1-4sin^2(18)+sin^2(18) = [/math]

[math]4sin^4(18)-3sin^2(18)+1... (2)[/math]

Now, we only have to evaluate [math]sin18[/math

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