Question

$tan{7}^{\circ }tan{23}^{\circ }tan{60}^{\circ }tan{67}^{\circ }tan{83}^{\circ }=$

• A. $\frac{1}{\sqrt{2}}$
• B. $\sqrt{3}$
• C. $\frac{1}{\sqrt{3}}$
• D. $0$

Answer 1

The correct option is B $\sqrt{3}$

$\Rightarrow tan{7}^{\circ }tan{23}^{\circ }tan{60}^{\circ }tan{67}^{\circ }tan{83}^{\circ }$

$=tan{7}^{\circ }tan{83}^{\circ }.tan{23}^{\circ }.tan({90}^{\circ }-{23}^{\circ }).tan{60}^{\circ }$

$=(tan{7}^{\circ }.cot{7}^{\circ }).(tan{23}^{\circ }.cot{23}^{\circ }).tan{60}^{\circ }$

$[\because tan({90}^{\circ }-\theta )=cot\theta ]$

$=1\times 1\times \sqrt{3}=\sqrt{3}$

$[\because tan\theta .cot\theta =1andtan{60}^{\circ }=\sqrt{3}]$