costheta=1/2(x+1/x) যদি হয়, তবে cos2θ= কত?

Explanation:

Another Explanation (5): দেওয়া আছে, \( \cos\theta = \frac{1}{2} \left( x + \frac{1}{x} \right) \) আমরা জানি, \( \cos2\theta = 2\cos^2\theta - 1 \) সুতরাং, \( \cos2\theta = 2 \left[ \frac{1}{2} \left( x + \frac{1}{x} \right) \right]^2 - 1 \) \( \Rightarrow \cos2\theta = 2 \cdot \frac{1}{4} \left( x^2 + 2 \cdot x \cdot \frac{1}{x} + \frac{1}{x^2} \right) - 1 \) \( \Rightarrow \cos2\theta = \frac{1}{2} \left( x^2 + 2 + \frac{1}{x^2} \right) - 1 \) \( \Rightarrow \cos2\theta = \frac{1}{2}x^2 + 1 + \frac{1}{2x^2} - 1 \) \( \Rightarrow \cos2\theta = \frac{1}{2}x^2 + \frac{1}{2x^2} \) \( \Rightarrow \cos2\theta = \frac{1}{2} \left( x^2 + \frac{1}{x^2} \right) \) অতএব, \( \cos2\theta = \frac{1}{2} \left( x^2 + \frac{1}{x^2} \right) \) 🥳