91Ó°ÊÓ

For Questions 4 through 6, determine if the statement is true or false. The sine of twice an angle equals twice the sine of the angle.

Let \(\tan \theta=3\) with \(\theta\) in QI and find the following. $$ \csc 2 \theta $$

$$ \text { Use half-angle formulas to find exact values for each of the following. } $$ \(\cos 105^{\circ}\)

Show that each of the following is true. $$ \sin \left(180^{\circ}-\theta\right)=\sin \theta $$

Use exact values to show that each of the following is true. $$ \cos 90^{\circ}=1-2 \sin ^{2} 45^{\circ} $$

Simplify each of the following. $$ \frac{\tan 112.5^{\circ}}{1-\tan ^{2} 112.5^{\circ}} $$

Prove the following identities. \(\sin ^{2} \frac{\theta}{2}=\frac{\csc \theta-\cot \theta}{2 \csc \theta}\)

Prove each identity. $$ \cos \left(x+90^{\circ}\right)+\cos \left(x-90^{\circ}\right)=0 $$

Evaluate without using a calculator or tables. \(\cos (\arctan 2)\)

Give the exact value of each of the following.\(\cos \frac{\pi}{6}\)