# Precalculus: trigonometry questions and answers

Recent questions in Trigonometry

### Prove that $$\displaystyle{\left({\cos{{A}}}+{\sin{{A}}}\right)}{\left({\cos{{2}}}{A}+{\sin{{2}}}{A}\right)}={\cos{{A}}}+{\sin{{3}}}{A}$$

Jessie Lee 2022-01-17

### Show that $$\displaystyle{I}{m}{\left({\frac{{{e}^{{{i}\theta}}}}{{{1}-{x}{e}^{{{i}\theta}}}}}\right)}={\frac{{{\sin{{\left(\theta\right)}}}}}{{{x}^{{2}}-{2}{x}{\cos{{\left(\theta\right)}}}+{1}}}}$$

Alan Smith 2022-01-17

### Find the minimum value of the function $$\displaystyle{\frac{{{\sin{{5}}}{x}}}{{{{\sin}^{{5}}{x}}}}}$$

idiopatia0f 2022-01-17

### How to evaluate: $$\displaystyle{{\cos{{24}}}^{{\circ}}-}{{\cos{{84}}}^{{\circ}}-}{{\cos{{12}}}^{{\circ}}+}{{\sin{{42}}}^{{\circ}}}$$

Pamela Meyer 2022-01-17

### Help me prove the exponential inequality $$\displaystyle{2}^{{{{\sin}^{{2}}{x}}}}+{2}^{{{{\cos}^{{2}}{x}}}}\leq{3}$$ I've reduced it to this: $$\displaystyle{2}^{{t}}+{2}^{{{1}-{t}}}\leq{3}$$ where $$\displaystyle{t}={{\sin}^{{2}}{x}}$$ and I also did a proof that is not elegant at all and kind of informal, I think that my brain after seeing this equation for so long as just frozen and won't do anything.

Joan Thompson 2022-01-17