Find the exact value of the expression \tan[\cos^{-1}(-\frac{\sqrt{3}}{2})]ZS

Let P(x, y) be the terminal point on the unit circle determined by t. Then $\sin t=,\cos t=,\text{and}\tan t=$.

How to simplify $(\cos x-\sin x)(2\tan x+\frac{1}{\cos x})+2=0$ to get a general solution?

I am trying to find a bound for ${\displaystyle \left|\cos (2n+1)\theta \right|}$ by something of the form ${\displaystyle c\left(n\right)\left|\cos \theta \right|}$ . I am suspecting that we can bound it by ${\displaystyle (2n+1)\left|\cos \theta \right|}$ but I'm not sure how to show that this is true

Find maximum of ${\displaystyle f\left(x\right)=3\cos \left\{2x\right\}+4\sin \left\{2x\right\}}$

Integrate from 0 to ${\displaystyle 2\pi }$ with respect to ${\displaystyle \theta }$ the following ${\displaystyle {(\sin \theta +\cos \theta )}^n}$

Deducing $\cos \theta <\frac{\sin \theta }{\theta }<1$ from $\sin \theta <\theta <\frac{\sin \theta }{\cos \theta }$

How do you simplify and evaluate ${\displaystyle \frac{{\tan 80}^{\circ }-{\tan 20}^{\circ }}{1+{\tan 80}^{\circ }{\tan 20}^{\circ }}}$