# Trigonometry Questions

## Express the trigonometric ratios sin A, sec A, and tan A in terms of cot A.

Solution : We know that   $$cosec^2 A$$ = 1 + $$cot^2 A$$ $$\implies$$   $$1\over sin^2 A$$ = 1 + $$cot^2 A$$   $$\implies$$  $$sin^2 A$$ = $$1\over 1 + cot^2 A$$ $$\implies$$  sin A = $$1\over \sqrt{1 + cot^2 A}$$ Also,  we know that  $$sec^2 A$$ = 1 + $$tan^2 A$$ $$\implies$$  $$sec^2 A$$ = 1 …

## Express sin 67 + cos 75 in terms of trigonometric ratios of angles between 0 and 45.

Solution : We have, sin 67 + cos 75 = sin(90 – 23) + cos(90 – 15) = cos 23 + sin 15

## If tan A = cot B, prove that A + B = 90.

Solution : We have,  tan A = cot B $$\implies$$  tan A = tan(90 – B) $$\implies$$  A = 90 – B $$\implies$$  A + B = 90

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

Solution : Given,   tan 2A = cot(A – 18) $$\implies$$  cot(90 – 2A) = cot(A – 18) $$\implies$$  90 – 2A = A – 18 $$\implies$$  3A = 108 $$\implies$$  A = 36