cos20⁰ cos40⁰ cos60⁰ cos80⁰= কত?

Explanation:

Another Explanation (5): cos20° cos40° cos60° cos80° -এর মান নির্ণয়: আমরা জানি, cos60° = 1/2 সুতরাং, cos20° cos40° cos60° cos80° = cos20° cos40° (1/2) cos80° = (1/2) cos20° cos40° cos80° এখন, cos20° cos40° cos80° = (cos20° cos40°) cos80° আমরা জানি, 2cosA cosB = cos(A+B) + cos(A-B) সুতরাং, cos20° cos40° = (1/2) [cos(20°+40°) + cos(20°-40°)] = (1/2) [cos60° + cos(-20°)] = (1/2) [cos60° + cos20°] ∵ [cos(-θ) = cosθ] = (1/2) [1/2 + cos20°] = 1/4 + (1/2) cos20° অতএব, cos20° cos40° cos80° = (1/2) [1/2 + cos20°] cos80° = (1/4) cos80° + (1/2) cos20° cos80° = (1/4) cos80° + (1/2) * (1/2) [cos(20°+80°) + cos(20°-80°)] = (1/4) cos80° + (1/4) [cos100° + cos(-60°)] = (1/4) cos80° + (1/4) [cos100° + cos60°] = (1/4) cos80° + (1/4) cos100° + (1/4) * (1/2) = (1/4) cos80° + (1/4) cos(180°-80°) + 1/8 = (1/4) cos80° + (1/4) (-cos80°) + 1/8 ∵ [cos(180°-θ) = -cosθ] = (1/4) cos80° - (1/4) cos80° + 1/8 = 1/8 সুতরাং, cos20° cos40° cos60° cos80° = (1/2) cos20° cos40° cos80° = (1/2) * (1/8) = 1/16 সুতরাং, cos20° cos40° cos60° cos80° = 1/16 🎉