If , prove that =

Given:

Now, squaring both the sides, we get

⇒ p² = q² tan²θ …(1)

Now, solving LHS

Putting the value of p² in the above equation, we get

[∵ 1+ tan² θ = sec² θ]

(from Eq. (1))

[∵(a + b) (a – b) = (a² – b²)]

Now, we solve the RHS

[∵ 1+ tan² θ = sec² θ]

∴ LHS = RHS

Hence Proved