(2)/(√(2+√(2+2cos4x)))=? 

Explanation:

Another Explanation (5): প্রদত্ত রাশি: \(\frac{2}{\sqrt{2+\sqrt{2+2\cos4x}}}\) আমরা জানি, \(\cos2\theta = 2\cos^2\theta - 1\) সুতরাং, \(2\cos^2\theta = 1 + \cos2\theta\) এখন, \(2+2\cos4x = 2(1+\cos4x) = 2(2\cos^2 2x) = 4\cos^2 2x\) তাহলে, \(\sqrt{2+\sqrt{2+2\cos4x}} = \sqrt{2+\sqrt{4\cos^2 2x}} = \sqrt{2+2|\cos 2x|}\) যদি \(\cos 2x \ge 0\) হয়, তবে \(\sqrt{2+2\cos 2x} = \sqrt{2(1+\cos 2x)} = \sqrt{2(2\cos^2 x)} = \sqrt{4\cos^2 x} = 2|\cos x|\) সুতরাং, \(\frac{2}{\sqrt{2+\sqrt{2+2\cos4x}}} = \frac{2}{2|\cos x|} = \frac{1}{|\cos x|}\) যদি \(\cos x > 0\) হয়, তবে \(\frac{1}{\cos x} = \sec x\) 🥳 অতএব, \(\frac{2}{\sqrt{2+\sqrt{2+2\cos4x}}} = \sec x\) 🤩