Write $\cos 50^{\circ }\cos 25^{\circ }+\sin 50^{\circ }\sin 25^{\circ }$ as a single trigonometric value of one angle.

Use a sum identity to find the exact value of $\sin 75^{\circ }$ in simplest radical form.

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

Write $\cos 10^{\circ }\cos 25^{\circ }-\sin 10^{\circ }\sin 25^{\circ }$ as a single trigonometric value of one angle.

Apply the sum identity to $\sin \left(x+\frac{3\pi }{4}\right)$ and substitute the exact values of the special angle. Which expression results?

Write $\sin 170^{\circ }\cos 10^{\circ }-\cos 170^{\circ }\sin 10^{\circ }$ as a single trigonometric value of one angle.

Use a difference identity to find the exact value of $\sin 15^{\circ }$ in simplest radical form.

Write $\cos 100^{\circ }\cos 5^{\circ }-\sin 100^{\circ }\sin 5^{\circ }$ as a single trigonometric value of one angle.

It is given that $\sin A=\frac{5}{13}$ with $A$ in the second quadrant, and that $\cos B=\frac{4}{5}$ with $B$ in the first quadrant. Find the exact value of $\sin (A-B)$.

Write $\sin 25^{\circ }\cos 10^{\circ }-\cos 25^{\circ }\sin 10^{\circ }$ as a single trigonometric value of one angle.

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

Use a sum identity to find the exact value of $\sin 255^{\circ }$ in simplest radical form.

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

The angle $\frac{19\pi }{12}$ is to be written as a sum or a difference of two angles whose sine and cosine are known exactly. Which pair does that?

It is given that $\sin A=\frac{9}{41}$ with $A$ in the first quadrant, and that $\cos B=\frac{12}{13}$ with $B$ in the first quadrant. Find the exact value of $\sin (A-B)$.

It is given that $\sin A=\frac{8}{17}$ with $A$ in the first quadrant, and that $\cos B=\frac{21}{29}$ with $B$ in the fourth quadrant. Find the exact value of $\cos (A-B)$.

Write $\sin 155^{\circ }\cos 50^{\circ }-\cos 155^{\circ }\sin 50^{\circ }$ as a single trigonometric value of one angle.

Apply the sum identity to $\sin \left(x+\frac{5\pi }{6}\right)$ and substitute the exact values of the special angle. Which expression results?

Use a sum identity to find the exact value of $\tan 75^{\circ }$ in simplest radical form.

The angle $\frac{11\pi }{12}$ is to be written as a sum or a difference of two angles whose sine and cosine are known exactly. Which pair does that?

The angle $\frac{17\pi }{12}$ is to be written as a sum or a difference of two angles whose sine and cosine are known exactly. Which pair does that?

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

Use a sum identity to find the exact value of $\cos 255^{\circ }$ in simplest radical form.

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

It is given that $\sin A=\frac{20}{29}$ with $A$ in the second quadrant, and that $\cos B=\frac{24}{25}$ with $B$ in the first quadrant. Find the exact value of $\cos (A+B)$.

Use a sum identity to find the exact value of $\cos 75^{\circ }$ in simplest radical form.

Write $\sin 140^{\circ }\cos 25^{\circ }-\cos 140^{\circ }\sin 25^{\circ }$ as a single trigonometric value of one angle.

Use a difference identity to find the exact value of $\tan 15^{\circ }$ in simplest radical form.

Apply the sum identity to $\sin \left(x+\frac{\pi }{6}\right)$ and substitute the exact values of the special angle. Which expression results?

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

It is given that $\sin A=\frac{3}{5}$ with $A$ in the second quadrant, and that $\cos B=\frac{40}{41}$ with $B$ in the fourth quadrant. Find the exact value of $\sin (A+B)$.

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

Apply the sum identity to $\sin \left(x+\frac{2\pi }{3}\right)$ and substitute the exact values of the special angle. Which expression results?

It is given that $\sin A=\frac{7}{25}$ with $A$ in the second quadrant, and that $\cos B=\frac{40}{41}$ with $B$ in the first quadrant. Find the exact value of $\sin (A+B)$.

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 $\sin (A+B)$.

Use a difference identity to find the exact value of $\cos 15^{\circ }$ in simplest radical form.

It is given that $\sin A=\frac{3}{5}$ with $A$ in the first quadrant, and that $\cos B=\frac{21}{29}$ with $B$ in the fourth quadrant. Find the exact value of $\sin (A+B)$.

It is given that $\sin A=\frac{20}{29}$ with $A$ in the second quadrant, and that $\cos B=\frac{15}{17}$ with $B$ in the fourth quadrant. Find the exact value of $\sin (A+B)$.

Write $\cos 155^{\circ }\cos 80^{\circ }+\sin 155^{\circ }\sin 80^{\circ }$ as a single trigonometric value of one angle.

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

The angle $\frac{13\pi }{12}$ is to be written as a sum or a difference of two angles whose sine and cosine are known exactly. Which pair does that?

Apply the sum identity to $\sin \left(x+\frac{\pi }{3}\right)$ and substitute the exact values of the special angle. Which expression results?

Apply the difference identity to $\sin \left(x-\frac{3\pi }{4}\right)$ and substitute the exact values of the special angle. Which expression results?

Use a sum identity to find the exact value of $\tan 165^{\circ }$ in simplest radical form.

Apply the difference identity to $\sin \left(x-\frac{\pi }{3}\right)$ and substitute the exact values of the special angle. Which expression results?

Use a sum identity to find the exact value of $\tan 195^{\circ }$ in simplest radical form.

Apply the difference identity to $\sin \left(x-\frac{5\pi }{6}\right)$ and substitute the exact values of the special angle. Which expression results?

The angle $\frac{23\pi }{12}$ 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 $\sin 40^{\circ }\cos 10^{\circ }-\cos 40^{\circ }\sin 10^{\circ }$ as a single trigonometric value of one angle.

Write $\sin 100^{\circ }\cos 65^{\circ }-\cos 100^{\circ }\sin 65^{\circ }$ as a single trigonometric value of one angle.