Inverse Trigonometric Functions
Compound Angles
Premium Question
Grade 12
Question:
The value of $\tan(\cos^{-1} \frac{3}{5} + \tan^{-1} \frac{1}{4})$ is:
(1) $\frac{19}{8}$
(2) $\frac{8}{19}$
(3) $\frac{17}{9}$
(4) $\frac{9}{17}$
Step-by-Step Solution
Key Concept: From $\cos^{-1}(3/5)$, read off $\tan$ using a right triangle. Then apply $\tan(A + B) = (\tan A + \tan B)/(1 - \tan A \tan B)$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)