A possible value of tan (1/4 sin ^-1 √63/8) is:

Question

A possible value of tan \((\frac{1}{4} sin^{-1} \frac{\sqrt{63}}{8})\) is

(1) \(\frac{1}{\sqrt7}\)

(2) 2√2 - 1

(3) √7 - 1

(4) \(\frac{1}{2\sqrt2}\)

Comments

IT IS BEST SOLUTION

Answer 1

Correct option is (A) \(\frac 1{\sqrt 7}\)

Let \(\sin^{-1} \left(\frac{\sqrt{63}}8\right) = \theta\)

⇒ \(\sin \theta =\frac{\sqrt{63}}8\)

So,

\(\tan \left(\frac 14 \sin^{-1} \frac{\sqrt{63}}8\right) = \tan \frac \theta 4\)

\(\cos \theta = \frac 18\)

⇒ \(2 \cos^2\frac \theta 2 - 1 = \frac 18\)

⇒ \( \cos^2\frac \theta 2 = \frac 9{16}\)

⇒ \(\cos \frac \theta 2 = \frac 34\)

⇒ \(\frac{1 - \tan^2\frac \theta 4}{1 + \tan^2\frac \theta 4} = \frac 34\)

\(\therefore \tan \frac \theta 4 = \frac 1{\sqrt 7}\)

Answer 2

The correct option is (1) \(\frac{1}{\sqrt7}\)