Evaluate the following integrals:

Since cosec x = 1/ sinx

Multiply with (1 + sinx) both numerator and denominator

Since (a + b) × (a - b) = a² - b²,

Let sinx = t

dt = cosx dx

therefore,

multiply and divide by 2 and add and subtract (1/2)² in denominator,

Let t + 1/2 = u

dt = du

Since,