MHT CET · Maths · Inverse Trigonometric Functions
Considering only the principal values of the inverse trigonometric functions, the value of \(\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)-2 \cos ^{-1}\left(\frac{2}{\sqrt{5}}\right)\right)\) is
- A \(\frac{7}{24}\)
- B \(\frac{-7}{24}\)
- C \(\frac{5}{24}\)
- D \(\frac{-5}{24}\)
Answer & Solution
Correct Answer
(B) \(\frac{-7}{24}\)
Step-by-step Solution
Detailed explanation
Let \( A = \sin^{-1}\left(\frac{3}{5}\right) \). Then \( \tan A = \frac{3}{4} \). Let \( B = \cos^{-1}\left(\frac{2}{\sqrt{5}}\right) \). Then \( \tan B = \frac{1}{2} \).
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