factor the expression and use the fundamental identities to simplify. There is more than one correct form of each answer.

$$\newline\sin^4x-\cos^4 x$$

Write the expression as the sine, cosine, or tangent of an angle.

$$\cos 45^{\circ} \cos 120^{\circ}-\sin 45^{\circ} \sin 120^{\circ}$$

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval $[0,2\pi).\newline$

$$2\tan^2x+7\tan x-15=0$$

factor the expression and use the fundamental identities to simplify. There is more than one correct form of each answer.

$$\newline1-2\cos^2x+2\cos^4 x$$

Verify the identity.

$$\sec ^4 x \tan ^2 x=\left(\tan ^2 x+\tan ^4 x\right) \sec ^2 x$$

Write the expression as the sine, cosine, or tangent of an angle.

$$\sin 60^{\circ} \cos 45^{\circ}-\cos 60^{\circ} \sin 45^{\circ}$$

Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle.

$$165^{\circ}$$

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval $[0,2\pi).\newline$

$$\csc^2x+0.5\cot x-5=0$$

Find the exact value of the trigonometric function given that $\sin u=-\frac{7}{25}$ and $\cos v=-\frac{4}{5}.$(Both $u$ and $v$ are in Quadrant $III.$)

$$\newline\csc(u-v)$$

factor the expression and use the fundamental identities to simplify. There is more than one correct form of each answer.

$$\newline\tan^4x+2\tan^2 x+1$$

Verify the identity.

$$\tan ^5 x=\tan ^3 x \sec ^2 x-\tan ^3 x$$

Find the exact value of the trigonometric function given that $\sin u=-\frac{7}{25}$ and $\cos v=-\frac{4}{5}.$(Both $u$ and $v$ are in Quadrant $III.$)

$$\newline\sec(v-u)$$

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval $[0,2\pi).\newline$

$$\sec^2x+0.5\tan x-1=0$$

Find the exact values of the sine, cosine, and tangent of the angle by using a sum or difference formula. $\frac{19 \pi}{12}=\frac{11 \pi}{6}-\frac{\pi}{4}$