Trigonometric Equations

Which of the following is equal to $8\cos x-8\cos (x-60^\circ) ?$

\sqrt{2}\cos (x+60^\circ)

4\cos (x+30^\circ)

4\cos (x+45^\circ)

8\cos (x+30^\circ)

8\cos (x+60^\circ)

What is the value of $\sin {56}^\circ-\sin {64}^\circ+\sin {176}^\circ ?$

If $\displaystyle x=\frac{\pi}{15}$ what is the value of $\frac{\cos x \cos 7x}{\cos 9x + \cos 7x} ?$

If $\displaystyle x=\frac{\pi}{96}$ what is the value of $\frac{\cos 14x + \cos 16x + \cos 18x}{\sin 14x + \sin 16x + \sin 18x} ?$

Which of the following expressions is equal to $7\sqrt{3}\sin \left(\theta+\frac{\pi}{3}\right)-14\cos \theta ?$

7\sin \left( \theta-\frac{\pi}{6} \right)

{7}\sqrt{2}\sin \left( \theta+\frac{\pi}{6} \right)

14\sin \left( \theta-\frac{\pi}{6} \right)

7\sin \left( \theta+\frac{\pi}{6} \right)

Trigonometric Equations - Sum to Product