Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
cosec2A - cot2A = 1
⇒ cosec2A = 1 + cot2A
⇒ 1/sin2A = 1 + cot2A
⇒sin2A = 1/(1+cot2A)
Now,
sin2A = 1/(1+cot2A)
⇒ 1 - cos2A = 1/(1+cot2A)
⇒cos2A = 1 - 1/(1+cot2A)
⇒cos2A = (1-1+cot2A)/(1+cot2A)
⇒ 1/sec2A = cot2A/(1+cot2A)
⇒ secA = (1+cot2A)/cot2A
also,
tan A = sin A/cos A and cot A = cos A/sin A
⇒ tan A = 1/cot A
