Evaluate

Multiplying numerator and denominator with 1-sinx

We get





Taking and


Solving for A


Taking cos x=t


On differentiating both sides we get


-sin x dx=dt


Putting values in A we get our equation as



= t-1+c


Substituting value of t,


=sec x + c


Solving for B



= ∫ sec2x - ∫ 1 dx


= tan x – x +c


Final answer is A+B


= sec x + tan x – x + c


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