Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions · Exercise 1

We know $g\left(x\right)=cosx$ is an even function, and $f\left(x\right)=sinx$ and $h\left(x\right)=tanx$ are odd functions. What about $G\left(x\right)=co{s}^{2}x,F\left(x\right)=si{n}^{2}x,$ and $H\left(x\right)=ta{n}^{2}x?$ Are they even, odd, or neither? Why?

OpenStax, Algebra and Trigonometry 2e · §9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions · Exercise 1