CUET · MATHS · PYQ PAPER 2023
The value of x given by \(\cos(\tan^{-1} x) = \sin(\cot^{-1} \frac{3}{4})\) is:
- A \(\frac{1}{4}\)
- B \(\frac{3}{4}\)
- C \(\frac{3}{2}\)
- D 1
Answer & Solution
Correct Answer
(B) \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
\(\sin(\cot^{-1} \frac{3}{4}) = \frac{4}{5}\) \(\cos(\tan^{-1} x) = \frac{1}{\sqrt{1+x^2}}\) \(\frac{1}{\sqrt{1+x^2}} = \frac{4}{5}\) \(1+x^2 = \frac{25}{16}\) \(x^2 = \frac{25}{16} - 1\) \(x^2 = \frac{9}{16}\) \(x = \frac{3}{4}\)
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