যদি sinθ+cosecθ=2 হয়, তবে sinⁿθ+cosecⁿθ=?

Explanation:

Another Explanation (5): দেওয়া আছে, \(sin\theta + cosec\theta = 2\) আমরা জানি, \(cosec\theta = \frac{1}{sin\theta}\) সুতরাং, \(sin\theta + \frac{1}{sin\theta} = 2\) উভয় দিকে \(sin\theta\) দিয়ে গুণ করে পাই, \(sin^2\theta + 1 = 2sin\theta\) \(sin^2\theta - 2sin\theta + 1 = 0\) \((sin\theta - 1)^2 = 0\) \(sin\theta - 1 = 0\) \(sin\theta = 1\) তাহলে, \(cosec\theta = \frac{1}{sin\theta} = \frac{1}{1} = 1\) এখন, \(sin^n\theta + cosec^n\theta = (1)^n + (1)^n = 1 + 1 = 2\) অতএব, \(sin^n\theta + cosec^n\theta = 2\)🎉