Taking LHS

Dividing by cosθ in numerator and denominator

Using and

Putting 1 = sec²θ - tan²θ in numerator

Using a² - b² = (a + b)(a - b)

= tan θ + sec θ

Now, taking RHS

Multiplying and dividing by secθ + tanθ = 1

= tanθ + secθ [As sec²θ - tan²θ = 1]

LHS = RHS

Hence Proved.