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.