A problem is a chance for you to do your best. – Duke Ellington

Question 16 $$\frac{\cos 9x – \cos 5x}{\sin 17x – \sin 3x} = – \frac{\sin 2x}{\cos 10x}$$

Question 17 $$\frac{\sin 5x + \sin 3x}{\cos 5x + \cos 3x} = \tan 4x$$

Question 18 $$\frac{\sin x – \sin y}{\cos x + \cos y} = \tan \frac{x-y}{2}$$

Question 19 $$\frac{\sin x + \sin 3x}{\cos x + \cos 3x} = \tan 2x$$

Question 20 $$\frac{\sin x – \sin 3x}{\sin^2 x – \cos^2 x} = 2 \sin x$$

Question 21 $$\frac{\cos 4x + \cos 3x + \cos 2x}{\sin 4x + \sin 3x + \sin 2x} = \cot 3x$$

Question 25 $$\cos 6x = 32 \cos^6 x – 48 \cos^4 x + 18 \cos^2 x – 1$$

Derivation for cot(A+B) and cot(A-B)

Question 22 $$\cot x \cot 2x – \cot 2x \cot 3x – \cot 3x \cot x = 1$$

Example 14 Show that $$\tan 3x \tan 2x \tan x = \tan 3x – \tan 2x –\tan x$$