Question 54

If $$x \sin 30^\circ \cos 60^\circ = \sin 45 \cos 45$$, then the value of $$x$$ is:

Solution

Given, $$x\sin30^{\circ}\cos60^{\circ}=\sin45\cos45$$

$$\Rightarrow$$ $$x\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{\sqrt{2}}\times\frac{1}{\sqrt{2}}$$

$$\Rightarrow$$ $$x\times\frac{1}{4}=\frac{1}{2}$$

$$\Rightarrow$$ $$x=2$$

Hence, the correct answer is Option A

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