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Determine if a trigonometric function is odd or even Precalculus

Determine if the following functions are even, odd, or neither of them.

f:x\longmapsto\sin\left(2x\right)-\cos\left(x\right)^2.\sin\left(x\right)

f:x\longmapsto \sin^2\left(2x\right)-\cos^2\left(x\right)

f:x\longmapsto \tan\left(x\right)+\cot\left(x\right)

f:x\longmapsto\cos\left(x\right)\sin^2\left(x\right)+\cos^3\left(x\right).\sin^4\left(x\right)

f\left(x\right) = \sin\left(x\right)+ \cos\left(x\right)

f\left(x\right) = \sin\left(x\right)\left[1-\cos\left(x\right)\right]

f\left(x\right)=\cos\left(x\right)\sin\left(x-\pi\right)+\cos\left(2x\right)\sin\left(x\right)