JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Considering only the principal values of inverse functions, the set \(A = \left\{ {x \geq \,:\,{{\tan }^{ - 1}}\,\left( {2x} \right) + {{\tan }^{ - 1}}\,\left( {3x} \right)\, = \frac{\pi }{4}} \right\}\)
- A contains two elements
- B contains more than two elements
- C is a singleton
- D is an empty set
Answer & Solution
Correct Answer
(C) is a singleton
Step-by-step Solution
Detailed explanation
\({\tan ^{ - 1}}2x + {\tan ^{ - 1}}3x = \frac{\pi }{2}\) Taking tangent on both side, we get \(\frac{{2x + 3x}}{{1 - 6{x^2}}} = 1\) \( \Rightarrow 6{x^2} + 5x - 1 = 0 \Rightarrow \left( {x + 1} \right)\left( {6x - 1} \right) = 0\) \( \Rightarrow x = \frac{1}{6}\) {\(-1\)is…
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