Evaluate of each of the following integral:

Let us assume ……………. equation 1


By property, we know that



We know that sec (2π – x) = sec (x)


tan(2π – x)=–tan (x)


thus
.......... equation 2


Adding equations 1 and equation 2, we get,



We know



Thus




We know Trigonometric identity sec2 x – tan2 x = 1



We know


where b is the upper limit and a is lower and f(x) is integral funtion



Thus I = 0.


2