1/cos²80° -3/cos²10° 化简
问题描述：
1/cos²80° -3/cos²10° 化简
答
[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
答
1/cos²80° -3/cos²10°=1/sin²10° -3/cos²10°=(cos²10° -3sin²10°)/(sin²10°·cos²10°)=16(1/4 *cos²10° -3/4 *sin²10°)/(2sin10°cos10°)²=16(c...