Mathematics

Problem

Answer the following without using a calculator. a. (i) Evaluate

A=\arcsin\left(\dfrac{3}{5}\right)+\arccos\left(\dfrac{4}{5}\right)

. Express your answer in radians. b. (ii) Evaluate

B=\arcsin\left(-\dfrac{12}{13}\right)+\arccos\left(-\dfrac{12}{13}\right)

. State the principal value obtained. c. (iii) Hence or otherwise, determine

C=\arcsin\left(\dfrac{3}{5}\right)+\arccos\left(-\dfrac{4}{5}\right)

and justify your result with reference to principal branches.