(tan5°-tan85°)(cos70°/1+cos20°) Such as the title

(tan5°-tan85°)(cos70°/1+cos20°) Such as the title

The original formula of cos20 = sin70 = (sin5 / cos5-cos5 / sin5) cos70 / (1 + sin70) = [(sin5) ^ 2 - (cos5) ^ 2] / sin5 / cos5 * cos70 / (1 + sin70) = - 2cos10 / sin10 * sin20 / (1 + sin70) = - 2cos10 / sin10 * sin10 * cos10 / (1 + sin70) = - 2 * (1 + cos20) / (1 + sin70) = - 2

Trigonometric transformation (tan5 ° - cot5 °) * sin20 ° / (1 + cos20 °)

(tan5 ° - cot5 °) is calculated as the root of the square
Sin20 ° / (1 + cos20 °): calculate 1 as the square of (cos20 ° + sin20 °)

(tan5-cot5)*sin20/(1+cos20)
5.20 is the angle
How did the masked prawns get to this level

(Tan 5-cot 5 degrees). Sin 20 degrees / (1 + cos 20 degrees)
Predigestion: Tan 5-cot 5 = (sin ^ 25-cos ^ 25) / sin 5cos 5 = 2 (sin ^ 25-cos ^ 25) / sin 10
Further simplification: (Tan 5-cot 5 degree). Sin 20 degree = 2 (sin ^ 25-cos ^ 25) / sin 10 * (2sin10cos 10) = 4 (sin ^ 25-cos ^ 25) * cos 10 = - 4cos ^ 210
Simplified denominator: 1 + cos20 degree = cos ^ 210 + sin ^ 210 + cos ^ 210-sin ^ 210 = 2cos ^ 210
So finally: (Tan 5 degrees - cot 5 degrees). Sin 20 degrees / (1 + cos 20 degrees) = - 4cos ^ 210 / 2cos ^ 210 = - 2