Mathematics

Problem

Angles

A

and

B

of a right-angled triangle satisfy

A + B = 90^\circ

. Given that

\sin A = \dfrac{5}{13}

, answer the following: (i) Find

\cos B

. (ii) Calculate

\tan A

and

\cot B

. (iii) Evaluate

\sin A + \sin B

and verify whether the value depends on the numerical choice of

A