JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
A possible value of \(\tan \left(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}\right)\) is :
- A \(\frac{1}{\sqrt{7}}\)
- B \(2 \sqrt{2}-1\)
- C \(\sqrt{7}-1\)
- D \(\frac{1}{2 \sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{7}}\)
Step-by-step Solution
Detailed explanation
Let \(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}=\theta\) \(\sin 4 \theta=\frac{\sqrt{63}}{8}\) \(\cos 4 \theta=\frac{1}{8}\) \(2 \cos ^{2} 2 \theta-1=\frac{1}{8}\) \(\cos ^{2} 2 \theta=\frac{9}{16}\) \(\cos 2 \theta=\frac{3}{4}\) \(2 \cos ^{2} \theta-1=\frac{3}{4}\)…
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