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$\sqrt 6 - \sqrt 3 - \sqrt 2 - 2$
$= \frac{{2\sin A\cos A}}{{2{{\cos }^2}A}} = \frac{{\sin 2A}}{{1 + {{\cos }^2}A}}$
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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