证明tan^2-sin^2=tan^2sin^2急用!

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/08 19:35:55

证明tan^2-sin^2=tan^2sin^2急用!
证明tan^2-sin^2=tan^2sin^2
急用!

证明tan^2-sin^2=tan^2sin^2急用!
tan^2-sin^2-tan^2sin^2
=tan^2(1-sin^2) -sin^2
=tan^2cos^2-sin^2
=sin^2-sin^2
=0
所以tan^2-sin^2=tan^2sin^2

tan^2-sin^2= sin^2/ cos^2 - sin^2
=sin^2[(1/cos^2)-1]
=sin^2 * (1-cos^2)/cos^2
=tan^2sin^2

tan^2 - sin^2
= sin^2/cos^2 - sin^2
= (sin^2 - sin^2*cos^2) / (cos^2)
= sin^2(1 - cos^2) / (cos^2)
= sin^2(sin^2) / (cos^2)
= tan^2*sin^2

tan^2-sin^2=(sin^2-sin^2cos^2)/cos^2=sin^2(1-cos^2)/cos^2=sin^2*sin^2/cos^2=tan^2sin^2

证明:∵左边=tan^2-sin^2
= sin^2/cos2-sin^2
=sin^2(1/cos^2-1)
=sin^2(1/cos^2-cos^2/cos^2)
=sin^2(1-cos^2/cos^2)
=sin^2(sin^2/cos^2)
=sin^2tan^2
=右边
∴原式成立!