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Determine If Trig Functions Are Odd, Even, Or Neither

Is the sentence true or false?

A function is "even" when: f(x)=f(x)f\left(x\right)=f\left(-x\right) for all xx.

Determine either f(x)=secxf\left(x\right)=\sec x is odd, even, or neither.

Determine either f(x)=cosecxf\left(x\right)=\operatorname{cosec}x is odd, even, or neither.

Determine either f(x)=2cosxf\left(x\right)=2\cos x is odd, even, or neither.

Determine either f(x)=sinx+cosxf\left(x\right)=\sin x+\cos x is odd, even, or neither.

Determine either f(x)=tanx+cosxf\left(x\right)=\tan x+\cos x is odd, even, or neither.

Is the sentence true or false?

A function is "odd" when: f(x)=f(x)f\left(x\right)=-f\left(-x\right) for all xx.

Determine either f(x)=cotxf\left(x\right)=\cot x is odd, even, or neither.

Determine either f(x)=cosxf\left(x\right)=\cos x is odd, even, or neither.

Determine either f(x)=tanxf\left(x\right)=\tan x is odd, even, or neither.