Question

The value of $\frac{tan{45}^{\circ }}{sin{30}^{\circ }+cos{30}^{\circ }}$ is:

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

Answer 1

Answer: (A), (D)

The correct options are
A $\frac{2}{\sqrt{3}+1}$
D $\sqrt{3}-1$

$\frac{\tan 45°}{\sin 30°+\cos 30°}=\frac{1}{\frac{1}{2}+\frac{\sqrt{3}}{2}}=\frac{2}{1+\sqrt{3}}$

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

$=\frac{2(\sqrt{3}-1)}{2}$

$=\sqrt{3}-1$

Hence, the answer is $\sqrt{3}-1.$