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JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
A value of \(x\) satisfying the equation \(\sin \left[ {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right] = \cos \left[ {{{\tan }^{ - 1}}\,x} \right]\) , 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
\(\sin \left[ {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right] = \cos \left( {{{\tan }^{ - 1}}x} \right)\) \(\cot \lambda = 1 + x\) \(\tan \beta = x\) \(\sin \lambda = \cos \beta \) \(\frac{1}{{\sqrt {{x^2}} + 2x + 2}} = \frac{1}{{1\sqrt {1 + {x^2}} }}\)…
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