Determine whether the equation is correct by evaluating each side. Do not use a calculator. $\tan 30 ^ { \circ } = \frac { \sin 60 ^ { \circ } } { 1 + \sin 30 ^ { \circ } }$

Question

Quizplus · Accepted Answer

We know that $	an 30^{\circ} = \frac{1}{\sqrt{3}}$ and $\sin 60^{\circ} = \frac{\sqrt{3}}{2}$

Now, let's evaluate the right-hand side of the equation:

$$\frac{\sin 60^{\circ}}{1+\sin 30^{\circ}} = \frac{\frac{\sqrt{3}}{2}}{1+\frac{1}{2}} =\frac{\sqrt{3}}{2}\cdot\frac{2}{3}=\frac{\sqrt{3}}{3} $$

We can see that the left-hand side and the right-hand side of the given equation are equal:

$$	an 30^\circ =\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3} = \frac{\sin 60 ^ { \circ } } { 1 + \sin 30 ^ { \circ } }$$

Therefore, the equation is true, and the answer is A.

Determine Whether the Equation Is Correct by Evaluating Each Side tan⁡30∘=sin⁡60∘1+sin⁡30∘\tan 30 ^ { \circ } = \frac { \sin 60 ^ { \circ } } { 1 + \sin 30 ^ { \circ } }tan30∘=1+sin30∘sin60∘​

Determine Whether the Equation Is Correct by Evaluating Each Side $\tan 30 ^ { \circ } = \frac { \sin 60 ^ { \circ } } { 1 + \sin 30 ^ { \circ } }$