Calc 2, Fall 2022 Problem Set 2 2. Using the substitution 0 = 2 arctan t, it is possible to transform any rational function of trig functions into a rational function of t, and hence use partial fractions. In this problem, you will use this substitution to (almost) find an antiderivative of cos 0 + sin 0 a) Using the double-angle identity cos(24) = 2 (cos 4) -1, and a triangle representing tan y = , it is possible to find that cos 0 = 2 (1! ) -1=1-t2 1 + t2 . Find a similar formula for sin 0. (b) Find a formula for de. (c) Plug the results of (a) and (b) in appropriately to find a new form of the integral which does not make any reference to trigonometric functions. Simplify the integrand completely. (d) Explain in one or two complete sentences how you would proceed to finish the problem. You do not need to work through the details, but the description should be sufficient that a fictional ideal classmate could finish the