Two acute angles and have the values and

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

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. (i) Find

\sin A

\tan A

and

\sec A

. (ii) Find

\sin B

\tan B

and

\sec B

. (iii) Hence determine the exact value of

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