cos²30°+cos²60°+ ............ + cos²180°=?

Explanation:

Another Explanation (5): প্রদত্ত রাশিটি হল: cos²30° + cos²60° + cos²90° + cos²120° + cos²150° + cos²180° আমরা জানি, cos(180° - θ) = -cos(θ) সুতরাং, cos²30° = (√3/2)² = 3/4 cos²60° = (1/2)² = 1/4 cos²90° = (0)² = 0 cos²120° = cos²(180° - 60°) = (-cos60°)² = (1/2)² = 1/4 cos²150° = cos²(180° - 30°) = (-cos30°)² = (√3/2)² = 3/4 cos²180° = (-1)² = 1 এখন, রাশিটির মান হবে: 3/4 + 1/4 + 0 + 1/4 + 3/4 + 1 = (3/4 + 1/4 + 1/4 + 3/4) + 1 = (3+1+1+3)/4 + 1 = 8/4 + 1 = 2 + 1 = 3 অতএব, cos²30° + cos²60° + cos²90° + cos²120° + cos²150° + cos²180° = 3 \( \boxed{3} \) 🎉🎉