Complete the Identity. sec( α.+ β ) sec( α.- β )

Question

Precalculus 

Answer 1

Greetings! Lets solve this shall we ?

So, we must solve this expression of sec(α+β)sec(α-β)............Using the Supplemental Angle Identities such that

sec(α+β) = -secθ and

sec(α-β) = -secθ. We obtain

sec(α+β)sec(α-β) = (-secθ)(-secθ) = sec²θ = tan²θ + 1

I hope this helped!