1)

Derivative of log (sec θ+ tan θ)  with respect to secθ  at θ =π4


A) 0

B) 1

C) 12

D) 2

Answer:

Option B

Explanation:

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