Question

If sec A - tan A = p and cosec A + cot A = q , then express p in terms of q and q in terms of p.

Answer 1

p = 1/(cos a) - (sin a)/(cos a)
q = 1/(sin a) - (cos a)/(sin a)

p * cos a = 1- (sin a)
q * sin a = 1 - (cos a)

p(cos a) + (sin a) = q(sin a) + (cos a)
Cos a (p - 1) = sin a (q - 1)
(p-1)/(q-1) = tan (a)

p-1 = tan(a) (q-1)
p = tan(a) (q-1) + 1

(p-1)/(q-1) = tan (a)
q-1 = (p-1)/tan (a)
q = (p-1)/tan(a) + 1