If sec(theta) + tan(theta) = p, then find tha value of cosec(theta)

Sec²θ - tan²θ = 1

(secθ + tanθ)( secθ - tanθ) = 1

p( secθ - tanθ) = 1

( secθ - tanθ) = 1/p and, ......-(1)

( secθ + tanθ) = p ..... - (2)

(1) + (2),

secθ = 1/2 (p + 1/p) ,

(2) - (1)

tanθ = 1/2 (p-1/p)

secθ / tanθ = cosecθ

Hence,

cosecθ = p +1/p / p-1/p = p² +1 / p² -1