Evaluate:

(i)

(ii)

(iii) Cos 48° – sin 42°

(iv) Cosec 31° – sec 59°

Show that:

(i) tan 48° tan 23° tan 42° tan 67° = 1

(ii) cos 38° Cos 52° – sin 38° sin 52° = 0

If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A

If tan A = cot B, prove that A + B = 90°

If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A

If A, B and C are interior angles of a triangle ABC, then show that

Express sin 67° + Cos 75° in terms of trigonometric ratios of angles between 0° and 45°