cosec10°- 4sin70° এর মান কত? 

🤔প্রশ্ন: cosec10° - 4sin70° = ?

আমরা জানি, cosecθ = 1/sinθ সুতরাং, cosec10° = 1/sin10°

দেওয়া আছে, cosec10° - 4sin70° = 1/sin10° - 4sin70°

আমরা জানি, sin(90° - θ) = cosθ সুতরাং, sin70° = sin(90° - 20°) = cos20°

তাহলে, 1/sin10° - 4cos20° = (1 - 4sin10°cos20°) / sin10°

এখন, 4sin10°cos20° = 2 * 2sin10°cos20° আমরা জানি, 2sinAcosB = sin(A+B) + sin(A-B) সুতরাং, 2sin10°cos20° = sin(10°+20°) + sin(10°-20°) = sin30° + sin(-10°) = sin30° - sin10° [∵ sin(-θ) = -sinθ] = 1/2 - sin10° [∵ sin30° = 1/2]

তাহলে, 4sin10°cos20° = 2 * (1/2 - sin10°) = 1 - 2sin10°

সুতরাং, (1 - 4sin10°cos20°) / sin10° = (1 - (1 - 2sin10°)) / sin10° = (1 - 1 + 2sin10°) / sin10° = 2sin10° / sin10° = 2 🎉

অতএব, cosec10° - 4sin70° = 2