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.
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.