Mathematics

Problem

Two acute angles

A

and

B

have the values

\cos A=\dfrac{4}{5}

and

\cos B=\dfrac{12}{13}

. Using only trigonometric relationships among the six basic ratios, evaluate a compound tangent expression. a. (i) Find

\sin A

\tan A

and

\sec A

. b. (ii) Find

\sin B

\tan B

and

\sec B

. c. (iii) Hence determine the exact value of

\dfrac{\tan A+\tan B}{1-\tan A\tan B}.