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