sin^2 10°+sin^2 20° +... +sin^2 80°+ sin^2 90° এর মান -- 

Explanation:

Another Explanation (5): bài toán: \(sin^2 10°+sin^2 20° +... +sin^2 80°+ sin^2 90° = ?\) আমরা জানি, \(sin(90° - θ) = cos θ\) সুতরাং, \(sin^2 10° = sin^2 (90° - 80°) = cos^2 80°\) \(sin^2 20° = sin^2 (90° - 70°) = cos^2 70°\) \(sin^2 30° = sin^2 (90° - 60°) = cos^2 60°\) \(sin^2 40° = sin^2 (90° - 50°) = cos^2 50°\) এখন, প্রদত্ত রাশিমালাটিকে এভাবে লেখা যায়: \(sin^2 10°+sin^2 20° +sin^2 30°+sin^2 40°+sin^2 50°+sin^2 60°+sin^2 70°+sin^2 80°+ sin^2 90°\) \(= (sin^2 10° + sin^2 80°) + (sin^2 20° + sin^2 70°) + (sin^2 30° + sin^2 60°) + (sin^2 40° + sin^2 50°) + sin^2 90°\) \(= (cos^2 80° + sin^2 80°) + (cos^2 70° + sin^2 70°) + (cos^2 60° + sin^2 60°) + (cos^2 50° + sin^2 50°) + sin^2 90°\) আমরা জানি, \(sin^2 θ + cos^2 θ = 1\) সুতরাং, \(= 1 + 1 + 1 + 1 + sin^2 90°\) \(= 4 + (1)^2\) [∵ sin 90° = 1] \(= 4 + 1\) \(= 5\) অতএব, \(sin^2 10°+sin^2 20° +... +sin^2 80°+ sin^2 90°\) এর মান 5।🥳🎉