m = tanθ+sinθ এবং n = tanθ - sinθ হলে, m²-n²=?

Explanation:

Another Explanation (5): দেওয়া আছে, m = tanθ + sinθ n = tanθ - sinθ তাহলে, m² - n² = (m + n)(m - n) = (tanθ + sinθ + tanθ - sinθ)(tanθ + sinθ - tanθ + sinθ) = (2tanθ)(2sinθ) = 4tanθsinθ ...(1) এখন, mn = (tanθ + sinθ)(tanθ - sinθ) = tan²θ - sin²θ = \(\frac{sin^2 θ}{cos^2 θ}\) - sin²θ = sin²θ(\(\frac{1}{cos^2 θ}\) - 1) = sin²θ(\(\frac{1 - cos^2 θ}{cos^2 θ}\)) = sin²θ(\(\frac{sin^2 θ}{cos^2 θ}\)) = sin²θ tan²θ সুতরাং, \( \sqrt{mn} = \sqrt{sin^2 θ tan^2 θ} \) = sinθ tanθ তাহলে, 4\( \sqrt{mn} \) = 4sinθ tanθ ...(2) (1) এবং (2) নং থেকে পাই, m² - n² = 4\( \sqrt{mn} \) অতএব, m² - n² = 4\( \sqrt{mn} \) ✅