Question 72

If $$2x=\sin\theta$$ and $$\frac{2}{x}=\cos\theta$$, then the value of $$4\left(x^2+\frac{1}{x^2}\right)$$ is:

Solution

Given, $$2x=\sin\theta$$ and $$\frac{2}{x}=\cos\theta$$

From the trigonometric identities,

$$\sin^2\theta\ +\cos^2\theta\ =1$$

$$\Rightarrow$$ $$\left(2x\right)^2+\left(\frac{2}{x}\right)^2=1$$

$$\Rightarrow$$ $$4x^2+\frac{4}{x^2}=1$$

$$\Rightarrow$$ $$4\left(x^2+\frac{1}{x^2}\right)=1$$

Hence, the correct answer is Option A

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