Question

$\frac{1}{sin{10}^o}-\frac{\sqrt{3}}{cos{10}^o}=4$

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{1}{\sin {10}^{\circ }}-\frac{\sqrt{3}}{\cos {10}^{\circ }}$

$=2(\frac{1}{2\sin {10}^{\circ }}-\frac{\sqrt{3}}{2\cos {10}^{\circ }})$

We know that $\sin {30}^{\circ }=\frac{1}{2}$ and $\cos {30}^{\circ }=\frac{\sqrt{3}}{2}$

$=2(\frac{1}{2}\sin {10}^{\circ }-\frac{\sqrt{3}}{2}\cos {10}^{\circ })$

$=2(\sin {30}^{\circ }\sin {10}^{\circ }-\cos {30}^{\circ }\cos {10}^{\circ })$

$=-2(\cos {30}^{\circ }\cos {10}^{\circ }-\sin {30}^{\circ }\sin {10}^{\circ })$

$=-2\left(\cos (30+10)\right)$

$=-2\cos {40}^{\circ }\ne 4$

Hence the statement is false.