Problem:
Maclaurin series to provide proof
Please help me with step by step solutions to the following problems.
1a. Prove
tan^-1 x + tan^-1 y = tan^-1 ((x+y)/(1-xy))
where -PI/2 < tan^-1 x + tan^-1 y < PI/2 .
Hint: Use an identity for tan(x+y).
1b. Use part (a) to show that
tan^-1 (1/2) + tan^-1 (1/3) = PI/4 .
1c. Use the first four terms of the Maclaurin series of tan^-1 x and part (b) to approximate the value of PI.