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GUJCET · Maths · Inverse Trigonometric Functions

\(\sin ^{-1}\left(\frac{3}{5}\right)-\sin ^{-1}\left(\frac{8}{17}\right)=\) ____________

  1. A \(\sin ^{-1} \frac{24}{85}\)
  2. B \(\cos ^{-1} \frac{84}{85}\)
  3. C \(\cos ^{-1} \frac{24}{85}\)
  4. D \(\sin ^{-1} \frac{84}{85}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\cos ^{-1} \frac{84}{85}\)

Step-by-step Solution

Detailed explanation

\(\sin^{-1} \left(\frac{3}{5}\right)-\sin^{-1} \left(\frac{8}{17}\right) = \sin^{-1} \left(\frac{3}{5}\sqrt{1-\left(\frac{8}{17}\right)^2} - \frac{8}{17}\sqrt{1-\left(\frac{3}{5}\right)^2}\right)\) \(= \sin^{-1} \left(\frac{3}{5} \cdot \frac{15}{17} - \frac{8}{17} \cdot \frac{4}{5}\right)\)