Question

Find the value of $\cot {45}^o+\cot {30}^o+\sin {150}^o$

• A. $\frac{3+\sqrt{3}}{2}$
• B. $\frac{3+2\sqrt{3}}{2}$
• C. $\frac{3-\sqrt{3}}{2}$
• D. $\frac{3-2\sqrt{3}}{2}$

Answer 1

The correct option is B $\frac{3+2\sqrt{3}}{2}$

The value of $\cot {45}^o+\cot {30}^o+\sin {150}^o$
$=\cot {45}^o+\cot {30}^o+\sin ({180}^o-{30}^o)$
$=\cot {45}^o+\cot {30}^o+\sin \left({30}^o\right)$

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

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

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