AP 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
- A \(\frac{3}{65}\)
- B \(\frac{-36}{65}\)
- C \(\frac{-33}{65}\)
- D \(-1\)
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…
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