# 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 + $$1\over cot^2 A$$

$$\implies$$  $$sec^2 A$$ = $$cot^2 A + 1\over cot^2 A$$

$$\implies$$  sec A = $$\sqrt{cot^2 A + 1}\over cot A$$

Also, we know that, tan A = $$1\over cot A$$