If $$2x=\sin\theta$$ and $$\frac{2}{x}=\cos\theta$$, then the value of $$4\left(x^2+\frac{1}{x^2}\right)$$ is:
Given, $$2x=\sin\theta$$ and $$\frac{2}{x}=\cos\theta$$
From the trigonometric identities,
$$\sin^2\theta\ +\cos^2\theta\ =1$$
$$\Rightarrow$$ $$\left(2x\right)^2+\left(\frac{2}{x}\right)^2=1$$
$$\Rightarrow$$Â $$4x^2+\frac{4}{x^2}=1$$
$$\Rightarrow$$Â $$4\left(x^2+\frac{1}{x^2}\right)=1$$
Hence, the correct answer is Option A
Create a FREE account and get:
