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TS EAMCET · Maths · Inverse Trigonometric Functions

If \(\cos ^{-1}\left(\frac{5}{13}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\cos ^{-1} x\), then \(x\) is equal to

  1. A \(\frac{3}{65}\)
  2. B \(\frac{-36}{65}\)
  3. C \(\frac{-33}{65}\)
  4. D \(-1\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{-33}{65}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \cos ^{-1}\left(\frac{5}{13}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\cos ^{-1} x \\ & =\cos ^{-1}\left[\frac{5}{13} \cdot \frac{3}{5}-\sqrt{1-\frac{25}{169}} \cdot \sqrt{1-\frac{9}{25}}\right]=\cos ^{-1} x \\ & \Rightarrow \quad \cos…