The value of 10^ -√3 10^ is equal to :

Question

The value of $\csc {10}^{\circ }-\sqrt{3}\sec {10}^{\circ }$ is equal to :

Accepted Answer

$\csc {10}^{\circ }-\sqrt{3}\sec {10}^{\circ }$

$\begin{gathered} =\frac{1}{\sin {10}^{\circ }}-\frac{\sqrt{3}}{\cos {10}^{\circ }} \ =\frac{\cos {10}^{\circ }-\sqrt{3}\sin {10}^{\circ }}{\sin {10}^{\circ }\cos {10}^{\circ }} \ =4[\frac{\frac{1}{2}\cos {10}^{\circ }-\frac{\sqrt{3}}{2}\sin {10}^{\circ }}{2\sin {10}^{\circ }\cos {10}^{\circ }}] \ =4[\frac{\sin ({30}^{\circ }-{10}^{\circ })}{\sin {20}^{\circ }}] \ =4 \end{gathered}$

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