cosec10°- 4sin70° এর মান কত? 

Explanation:

Another Explanation (5): cosec10° - 4sin70° এর মান নির্ণয়: আমরা জানি, cosecθ = 1/sinθ সুতরাং, cosec10° = 1/sin10° তাহলে, cosec10° - 4sin70° = 1/sin10° - 4sin70° sin70° = cos(90° - 70°) = cos20° সুতরাং, 1/sin10° - 4cos20° = (1 - 4cos20°sin10°)/sin10° এখন, 4cos20°sin10° = 2(2cos20°sin10°) আমরা জানি, 2sinAcosB = sin(A+B) + sin(A-B) তাহলে, 2(2cos20°sin10°) = 2[sin(20°+10°) + sin(20°-10°)] = 2[sin30° + sin10°] = 2sin30° + 2sin10° = 2 * (1/2) + 2sin10° [ যেহেতু sin30° = 1/2] = 1 + 2sin10° অতএব, (1 - 4cos20°sin10°)/sin10° = (1 - (1 + 2sin10°))/sin10° = (1 - 1 - 2sin10°)/sin10° = (-2sin10°)/sin10° = -2 ❌ মনেকরি অঙ্কটিতে কোথাও ভুল আছে। 🤔 আবার চেষ্টা করি। cosec10° - 4sin70° = 1/sin10° - 4cos20° [∵ sin70° = cos20°] = (1 - 4sin10°cos20°)/sin10° = (1 - 2(2sin10°cos20°))/sin10° = (1 - 2(sin(10° + 20°) + sin(10° - 20°)))/sin10° = (1 - 2(sin30° + sin(-10°)))/sin10° = (1 - 2(1/2 - sin10°))/sin10° [∵ sin(-θ) = -sinθ] = (1 - 1 + 2sin10°)/sin10° = (2sin10°)/sin10° = 2 ✅ সুতরাং, cosec10° - 4sin70° = 2