Question

$cot{12}^{\circ }cot{38}^{\circ }cot{52}^{\circ }cot{60}^{\circ }cot{78}^{\circ }=$

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

Answer 1

The correct option is C $\frac{1}{\sqrt{3}}$

$\Rightarrow cot{12}^{\circ }cot{38}^{\circ }cot{52}^{\circ }cot{60}^{\circ }cot{78}^{\circ }$

$=(cot{12}^{\circ }.cot{78}^{\circ }).(cot{38}^{\circ }.cot{52}^{\circ }).cot{60}^{\circ }$

$=\{cot{12}^{\circ }.cot({90}^{\circ }-{12}^{\circ }\left)\right\}\{cot{38}^{\circ }.cot({90}^{\circ }-{38}^{\circ }\left)\right\}.cot{60}^{\circ }$

$=(cot{12}^{\circ }.tan{12}^{\circ }).(cot{38}^{\circ }.tan{38}^{\circ }).cot{60}^{\circ }$

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

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