Rational functions of trigonometric functions An integrand with trigonometric functions in the numerator and denominator can often be converted to a rational integrand using the substitution u =tan (x/2) or x = 2 tan?1 u. The following relations are used in making this change of variables.A: B: C: Evaluate .

Problem 77ERational functions of trigonometric functionsAn integrand with trigonometric functions in the numerator and denominator can often be converted to a rational integrand using the substitution or The following relations are used in making this change of variables:A: B: C: Evaluate Solution:-Step 1Making the indicated substitutions in the integral, we get = = = = (Adding and subtracting 1 in denominator)= () = = = = = Substituting back the value of we get = Thus, the value of the integral is .