Question

if sec0+tan0=p,pt sec0-tan0=1/p

Answer 1

Solution -

Given: secθ + tanθ = p

We know that, tan^2θ + 1 = sec^2θ

Therefore, sec^2θ - tan^2θ = 1

(secθ + tanθ) (secθ - tanθ) = 1

p (secθ - tanθ) = 1

secθ - tanθ = 1/p

Hence proved. 

Answer 2

SecФ + tanФ = p
to prove:   secФ  - tan Ф  = 1/p

p =  (secФ + tanФ)
    = (secФ + tanФ) (sec Ф - tanФ)/(secФ - tanФ)
    = (sec² Ф - tan²Ф) / ( secФ - tanФ)
p = 1/(secФ - tanФ)

secФ - tanФ = 1/p