1) Derivative of log (sec θ+ tan θ) with respect to secθ at θ =π4 A) 0 B) 1 C) 1√2 D) √2 Answer: Option BExplanation:Let u=log (sec θ+ tan θ) and v= secθ On differentiating both sides w.r.t θ , we get dudθ=1(secθ+tanθ)(secθtanθ+sec2θ) and dvdθ=secθtanθ ∴ dvdθ=dudθdvdθ = secθ(tanθ+secθ)(secθ+tanθ)×secθtanθ=cotθ ⇒ dudv(θ=π/4)=cotπ4=1