Question

Solve $\frac{\sin {30}^o+\tan {45}^o-\cos es{60}^o}{\sec {30}^o+\cos {60}^o+\cos {45}^o}$

Answer 1

We have,

$\frac{\sin {30}^{\circ }+\tan {45}^{\circ }-\cos ec{60}^{\circ }}{\sec {30}^{\circ }+\cos {60}^{\circ }+\cos {45}^{\circ }}$

$=\frac{\frac{1}{2}+1-\frac{2}{\sqrt{3}}}{\frac{2}{\sqrt{3}}+\frac{1}{2}+\frac{1}{\sqrt{2}}}$

$=\frac{\frac{\sqrt{3}+2\sqrt{3}-4}{2\sqrt{3}}}{\frac{4\sqrt{2}+\sqrt{2}\sqrt{3}+2\sqrt{3}}{2\sqrt{2}\sqrt{3}}}$

$=\frac{(\sqrt{3}+2\sqrt{3}-4)\sqrt{2}}{4\sqrt{2}+\sqrt{2}\sqrt{3}+2\sqrt{3}}$

$=\frac{(\sqrt{2}\sqrt{3}+2\sqrt{2}\sqrt{3}-4\sqrt{2})}{\sqrt{2}\sqrt{3}+2\sqrt{3}+4\sqrt{2}}$

Hence, the value is $\frac{(\sqrt{2}\sqrt{3}+2\sqrt{2}\sqrt{3}-4\sqrt{2})}{\sqrt{2}\sqrt{3}+2\sqrt{3}+4\sqrt{2}}$.