Question

Find the value of $\sqrt{3}\text{cosec}{20}^0-\sec {20}^0$

Answer 1

$\sqrt{3}cosec{20}^{\circ }-sec{20}^{\circ }=\left(\frac{\sqrt{3}}{sin{20}^{\circ }}\right)-\left(\frac{1}{cos{20}^{\circ }}\right)=\left(\frac{\sqrt{3}cos{20}^{\circ }-sin{20}^{\circ }}{sin{20}^{\circ }\times cos{20}^{\circ }}\right)=\left(\frac{\left(\frac{\sqrt{3}}{2}\right)cos{20}^{\circ }-\left(\frac{1}{2}\right)sin20}{2sin{20}^{\circ }\times cos{20}^{\circ }}\right)\times 4=\left(\frac{cos{30}^{\circ }cos{20}^{\circ }-sin{30}^{\circ }sin{20}^{\circ }}{sin{40}^{\circ }}\right)\times 4=\left(\frac{cos{50}^{\circ }}{sin{40}^{\circ }}\right)\times 4=\left(\frac{sin{40}^{\circ }}{sin{40}^{\circ }}\right)\times 4=1\times 4=4$