Question

$\frac{\cos 30°+\sin 60°}{1+\cos 60°+\sin 30°}$ is equals to:

• A. $\frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $1$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is D

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

Explanation for the correct option:

Putting up the values in given expression we have:

$\frac{\cos 30°+\sin 60°}{1+\cos 60°+\sin 30°}$

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

As, $\left[\cos 30°=\frac{\sqrt{3}}{2},\sin 30°=\frac{1}{2}\right]$ and$\left[\cos 60°=\frac{1}{2},\sin 60°=\frac{\sqrt{3}}{2}\right]$

Therefore,

$$\begin{gathered} =\frac{{\displaystyle \frac{2\sqrt{3}}{2}}}{{\displaystyle \frac{4}{2}}} \\ =\frac{\sqrt{3}}{2} \end{gathered}$$

Hence, option (D) is the correct answer.