MHT CET · Maths · Inverse Trigonometric Functions
Considering only the principal values of the inverse trigonometric function, the value of \(\tan \left(\cos ^{-1} \frac{1}{5 \sqrt{2}}-\sin ^{-1} \frac{4}{\sqrt{17}}\right)\) is
- A \(\frac{3}{34}\)
- B \(\frac{1}{34}\)
- C \(\frac{3}{29}\)
- D \(\frac{1}{29}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{29}\)
Step-by-step Solution
Detailed explanation
Let \( \alpha = \cos ^{-1} \frac{1}{5 \sqrt{2}} \). Then \( \tan \alpha = \frac{\sqrt{(5\sqrt{2})^2 - 1^2}}{1} = \frac{\sqrt{50-1}}{1} = 7 \). Let \( \beta = \sin ^{-1} \frac{4}{\sqrt{17}} \). Then \( \tan \beta = \frac{4}{\sqrt{(\sqrt{17})^2 - 4^2}} = \frac{4}{\sqrt{17-16}} = 4 \).
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