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  • A possible value of <img alt="\tan \left ( \frac{1}{4}\sin ^{-1}\frac{\sqrt{63}}{8} \right )" src="https://entrancecorner.codecogs.com/gif.latex?%5Ctan%20%5Cleft%20%28%20%5Cfrac%7B1%7D%7B4%7D%5Csin%20%5E%7B-1%7D%5Cfrac%7B%5Csqrt%7B63%7D%7D%7B8%7D%20%5C

A possible value of \tan \left ( \frac{1}{4}\sin ^{-1}\frac{\sqrt{63}}{8} \right ) is :
 
Option: 1 \frac{1}{2\sqrt{2}}
Option: 2 \sqrt{7}-1
Option: 3 \frac{1}{\sqrt{7}}
Option: 4 2\sqrt{2}-1

Answers (1)

best_answer

 

\\\text {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}

\\\cos ^{2} \theta=\frac{7}{8} \\ \\\cos \theta=\frac{\sqrt{7}}{2 \sqrt{2}} \\ \\\tan \theta=\frac{1}{\sqrt{7}}

Posted by

Suraj Bhandari

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