1/cos²80° -3/cos²10° 化简

1/cos²80° -3/cos²10° 化简
1/cos²80° -3/cos²10° 化简

1/cos²80° -3/cos²10° 化简
1/cos²80° -3/cos²10°
=1/sin²10° -3/cos²10°
=(cos²10° -3sin²10°)/(sin²10°·cos²10°)
=16(1/4 *cos²10° -3/4 *sin²10°)/(2sin10°cos10°)²
=16(cos10°*1/2 + sin10°*√3/2)(cos10°*1/2 - sin10°*√3/2)/sin²20°
=16*sin40°*cos70°/sin²20°
=32sin20°cos20°/sin20°
=32cos20°

[1/(cos80°)^2-3/(cos10°)^2]
=[(1/cos80 + √3/cos10) * (1/cos80 - √3/cos10)]
=[(1/sin10 + √3/cos10) * (1/sin10 - √3/cos10)]
=[(cos10+√3sin10)/sin10cos10 * (cos10-√3sin10)/sin10cos10]
=[4sin40/sin20 * 4cos70/sin20]
=[16sin40/sin20]
=32cos20