- 高一数学化简（1
- 化简（1-sin^6 a-c^6 a)/(1-sin^4 a-cos^4 a)
注:sin^6 a 表示sina的6次方.
请写出详细的过程,谢谢!!!!!!
- 3/2
∵ 1-sin^4 a-cos^4 a
=sin^2 a+cos^2 a-sin^4 a-cos^4 a
=sin^2 a(1-sin^2 a)+cos^2 a(1-cos^2 a)
=2sin^2 a cos^2 a
1-sin^6 a-cos^6 a
=1-(sin^2 a+cos^2 a)(sin^4 a+cos^4 a-sin^2 acos^2 a)
=1-sin^4 a-cos^4 a+sin^2 acos^2 a
=3sin^2 a cos^2 a
∴原式=3/2