If ∫ d θ cos 2 θ tan 2 θ + sec 2 θ = λ tan θ + 2 log e f θ + C where C is a constant of integration, then the ordered pair λ , f θ is equal to:

Question

If ∫ d θ cos 2 θ tan 2 θ + sec 2 θ = λ tan θ + 2 log e f θ + C where C is a constant of integration, then the ordered pair λ , f θ is equal to:, 1 , 1 - tan θ, - 1 , 1 - tan θ, - 1 , 1 + tan θ, 1 , 1 + tan θ

MARKS App · Accepted Answer

∫ sec 2 θ 1 + tan 2 θ 1 - tan 2 θ + 2 tan θ 1 - tan 2 θ d θ = ∫ sec 2 θ 1 - tan 2 θ 1 + t a n θ 2 d θ = ∫ sec 2 θ 1 - tan θ 1 + tan θ d θ Let tan θ = t ⇒ sec 2 θ d θ = d t = ∫ 1 - t 1 + t d t = ∫ - 1 + 2 1 + t d t = - t + 2 ln 1 + t + C = - tan θ + 2 ln 1 + tan θ + C ⇒ λ = - 1 a n d f θ = 1 + tan θ

Search any question & find its solution

Looking for more such questions to practice?