CUET · MATHS · PYQ PAPER 2023
\(\tan \left[\frac{1}{2} \cos ^{-1}\left(\frac{4}{5}\right)\right]=\)
- A \(\frac{1}{3}\)
- B \(\frac{1}{\sqrt{10}}\)
- C \(\frac{\sqrt{3}}{10}\)
- D 3
Answer & Solution
Correct Answer
(A) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
Let \(\theta = \cos^{-1}\left(\frac{4}{5}\right)\). Then \(\cos\theta = \frac{4}{5}\). We need to find \(\tan\left(\frac{\theta}{2}\right)\). \(\tan\left(\frac{\theta}{2}\right) = \sqrt{\frac{1 - \cos\theta}{1 + \cos\theta}}\)…
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