The value of 71 2 ^ is equal to - Vidyadip

MCQ

The value of $\tan 7\frac{1}{2}^\circ $ is equal to

A
$\sqrt 6 + \sqrt 3 + \sqrt 2 - 2$
✓
$\sqrt 6 - \sqrt 3 + \sqrt 2 - 2$
C
$\sqrt 6 - \sqrt 3 + \sqrt 2 + 2$
D
$\sqrt 6 - \sqrt 3 - \sqrt 2 - 2$

✓

Answer

Correct option: B.

$\sqrt 6 - \sqrt 3 + \sqrt 2 - 2$

b
(b) We have $\tan A = \frac{{\sin A}}{{\cos A}} $

$= \frac{{2\sin A\cos A}}{{2{{\cos }^2}A}} = \frac{{\sin 2A}}{{1 + {{\cos }^2}A}}$

Putting $A = 7{\frac{1}{2}^o} $

$\Rightarrow \tan 7{\frac{1}{2}^o} = \frac{{\sin {{15}^o}}}{{1 + \cos {{15}^o}}}$

On simplification, we get $\tan 7{\frac{1}{2}^o} = \sqrt 6 - \sqrt 3 + \sqrt 2 - 2$.

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