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 \( \tan 3x \tan 2x \tan x = \tan 3x – \tan 2x –\tan x \)