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JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
A value of \(x\) for which \(\sin \,\left( {{{\cot }^{ - 1}}\,\left( {1 + x} \right)} \right) = \cos \,\left( {{{\tan }^{ - 1}}\,x} \right)\), is
- A \( - \frac{1}{2}\)
- B \(1\)
- C \(0\)
- D \( \frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \( - \frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\sin \left( {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right) = \cos \left( {{{\tan }^{ - 1}}x} \right)\) \( \Rightarrow \cos e{c^2}\left( {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right) = {\sec ^2}\left( {{{\tan }^{ - 1}}x} \right)\)…
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