If (sec θ + tan θ) = m and (sec θ – tan θ) = n, show that mn = 1.

Question

Philoid · Accepted Answer

Given: (sec θ + tan θ) = m …………….(1)

(sec θ – tan θ) = n …………….(2)

Multiply equation (1) and (2):

(sec θ + tan θ) (sec θ – tan θ) = mn

(sec² θ – tan² θ) = mn

1 = mn (∵ 1 + tan² θ = sec² θ)

Therefore, mn = 1.

Hence, proved.