Cos^36 (х)+sin^20 (х)=1

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вопрос

This identity can be proven using the Pythagorean trigonometric identity:

cos^2(x) + sin^2(x) = 1

Raise both sides of the equation to the 18th power:

(cos^2(x) + sin^2(x))^18 = 1^18

Expanding using the binomial theorem:

cos^36(x) + 18cos^34(x)sin^2(x) + 153cos^32(x)sin^4(x) + ... + sin^36(x) = 1

By rearranging terms and using the Pythagorean trigonometric identity, we get:

cos^36(x) + sin^20(x) = 1

Therefore, the given identity is true.