化简(sin平方80°-sin平方10°)平方+cos平方70°的值为!在线等.
问题描述：
化简(sin平方80°-sin平方10°)平方+cos平方70°的值为!在线等.
答
(sin平方80°-sin平方10°)平方+cos平方70°
=[(sin80°)^2-(sin10°)^2]^2+(cos70°)^2
=[(sin80°-sin10°)(sin80°+sin10°)]^2+(cos70°)^2
={2cos[(80°+10°)/2]sin[(80°-10°)/2]2sin[(80°+10°)/2]cos[(80°-10°)/2]}^2+(cos70°)^2
={4cos45°sin35°sin45°cos35°)^2+(cos70°)^2
=(2sin35°cos35°)^2+(cos70°)^2
=[sin(2×35°)]^2+(cos70°)^2
=[sin70°)^2+(cos70°)^2
=1
答
(sin²80°-sin²10°)²+cos²70°
=(cos²10°-sin²10°)²+cos²70°
=cos²20°+sin²20°
=1
答
(sin平方80°-sin平方10°)平方+cos平方70°的值
=(sin²80°-cos²80°)²+cos²70°
=(-cos160°)²+cos²70°
=cos²20°+sin²20°
=1