A verification has reached $\frac{\sin \theta }{\cos \theta }\cos \theta$ and must arrive at $\sin \theta$. Which step gets it there?

Use a sum identity to find the exact value of $\cos 285^{\circ }$ in simplest radical form.

It is given that $\tan \alpha =-\frac{7}{6}$ and that $\alpha$ lies in the fourth quadrant. Find the exact value of $\tan 2\alpha$.

Simplify ${\sin }^2\theta +{\cos }^2\theta$.

Find every solution of $2{\sin }^{2}x+7\sin x+3=0$ on the interval $\left[0,2\pi \right)$.

Simplify $\cos \theta \tan \theta$.

Apply a sum or difference identity to $\sin \left(\frac{3\pi }{2}+x\right)$ and simplify the result.

It is given that $\sin A=\frac{8}{17}$ with $A$ in the first quadrant, and that $\cos B=\frac{24}{25}$ with $B$ in the first quadrant. Find the exact value of $\cos (A-B)$.

Find every solution of $\sin 3x=1$ on the interval $\left[0,2\pi \right)$.

Find every solution of $\cos \frac{x}{2}=-\frac{\sqrt{3}}{2}$ on the interval $\left[0,2\pi \right)$.

Find every solution of $2{\sin }^{2}x+5\sin x+2=0$ on the interval $\left[0,2\pi \right)$.

A verification has reached $\frac{{\sin }^2\theta }{\sin \theta }$ and must arrive at $\sin \theta$. Which step gets it there?

Find every solution of $2{\sin }^{2}x-5\sin x+2=0$ on the interval $\left[0,2\pi \right)$.

A verification has reached $\frac{\cos \theta }{1-\sin \theta }$ and must arrive at $\frac{1+\sin \theta }{\cos \theta }$. Which step gets it there?

The angle $\frac{5\pi }{12}$ is to be written as a sum or a difference of two angles whose sine and cosine are known exactly. Which pair does that?

Write the general solution of $\tan x=-\frac{\sqrt{3}}{3}$, taking $n$ to be any integer.

Find every solution of $\sec x=2$ on the interval $\left[0,2\pi \right)$.

Find every solution of $\sin 2x=\frac{\sqrt{3}}{2}$ on the interval $\left[0,2\pi \right)$.

Find every solution of ${\cos }^{2}x+\cos x-2=0$ on the interval $\left[0,2\pi \right)$.

Find every solution of $2{\sin }^{2}x+\cos x-1=0$ on the interval $\left[0,2\pi \right)$.

Find every solution of $\cos 3x=1$ on the interval $\left[0,2\pi \right)$.

Find every solution of $4{\sin }^{2}x-3=0$ on the interval $\left[0,2\pi \right)$.

A verification has reached $1-{\cos }^2\theta$ and must arrive at ${\sin }^2\theta$. Which step gets it there?

It is given that $\sin A=\frac{7}{25}$ with $A$ in the first quadrant, and that $\cos B=\frac{12}{13}$ with $B$ in the fourth quadrant. Find the exact value of $\cos (A-B)$.

Simplify $\sin \theta \cot \theta$.

Simplify $\sec \theta \sin \theta$.

Use a half-angle identity to find the exact value of $\cos 22.5^{\circ }$ in simplest radical form.

Given that $\cos \theta =\frac{21}{29}$ and $\theta$ lies in the first quadrant, find $\sin \theta$.

Find every solution of $2{\sin }^{2}x+\sin x-1=0$ on the interval $\left[0,2\pi \right)$.

Simplify $\frac{\left(\sec \theta -\tan \theta \right)\left(\sec \theta +\tan \theta \right)}{\sec \theta +\tan \theta }$.

Factor ${\sec }^2\theta -{\csc }^2\theta$.

Find every solution of $\cos \frac{x}{2}=-\frac{\sqrt{2}}{2}$ on the interval $\left[0,2\pi \right)$.

Find every solution of $\cos \theta =-\frac{1}{2}$ for $0^{\circ }\le \theta <360^{\circ }$.

Find every solution of $2{\cos }^{2}x+5\cos x+2=0$ on the interval $\left[0,2\pi \right)$.

Which single trigonometric value is equal to $\sqrt{\frac{1+\cos \pi }{2}}$?

A verification has reached $\left(\sec \theta -\tan \theta \right)\left(\sec \theta +\tan \theta \right)$ and must arrive at $1$. Which step gets it there?

Find every solution of $\csc x=\frac{2\sqrt{3}}{3}$ on the interval $\left[0,2\pi \right)$.

A verification has reached $\frac{1}{\cos \theta }\sin \theta$ and must arrive at $\tan \theta$. Which step gets it there?

Find every solution of $\cos x=-\frac{\sqrt{3}}{2}$ on the interval $\left[0,2\pi \right)$.

Find every solution of $2\sin x-\sqrt{2}=0$ on the interval $\left[0,2\pi \right)$.