Question

Please solve question 3

Answer 1

$\sf \Large Solution!!$

We should know the trigonometry ratio table.

$\sf \to \displaystyle \dfrac{\sin 30^{\circ}+\tan 45^{\circ}-\csc 60^{\circ}}{\sec 30^{\circ}+\cos 60^{\circ}+\cot 45^{\circ}}$

$\sf \to \dfrac{\dfrac{1}{2}+1-\dfrac{2}{\sqrt{3}}}{\dfrac{2}{\sqrt{3}}+\dfrac{1}{2}+1}$

$\sf \to \dfrac{\sqrt{3}+2\sqrt{3}-4}{4+\sqrt{3}+2\sqrt{3}}$

$\sf \to \dfrac{3\sqrt{3}-4}{3\sqrt{3+4}}\times \dfrac{3\sqrt{3}-4}{3\sqrt{3-4}}$

$\sf \to \dfrac{27-12\sqrt{3}-12\sqrt{3}+16}{27-16}$

$\sf \to \dfrac{43-24\sqrt{3}}{11}$