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Trigonometric Equations

Equations with trigonometry in them can look scary, but that's nothing that a quick little substitution can't fix.

Trigonometric Equations - Sum to Product


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

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 \[7\sqrt{3}\sin \left(\theta+\frac{\pi}{3}\right)-14\cos \theta ?\]


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