Question 65

If $$\sin(\theta+30^{\circ})=\frac{3}{\sqrt{12}}$$, then the value of $$\theta$$ is equal to:

Solution

Given,  $$\sin(\theta+30^{\circ})=\frac{3}{\sqrt{12}}$$

$$\Rightarrow$$  $$\sin(\theta+30^{\circ})=\frac{3}{2\sqrt{3}}$$

$$\Rightarrow$$  $$\sin(\theta+30^{\circ})=\frac{\sqrt{3}\times\sqrt{3}}{2\sqrt{3}}$$

$$\Rightarrow$$  $$\sin(\theta+30^{\circ})=\frac{\sqrt{3}}{2}$$

$$\Rightarrow$$  $$\sin(\theta+30^{\circ})=\sin60^{\circ\ }$$

$$\Rightarrow$$  $$\theta+30^{\circ}=60^{\circ\ }$$

$$\Rightarrow$$  $$\theta=30^{\circ\ }$$

Hence, the correct answer is Option C


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