化简(sin^2a-tan^2a)*(sin^2a*tan^2a)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 11:31:17

化简(sin^2a-tan^2a)*(sin^2a*tan^2a)
化简(sin^2a-tan^2a)*(sin^2a*tan^2a)

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

(sin^2a-tan^2a)*(sin^2a*tan^2a)
=sin^2a(1-sec^2a)*(sin^2a*tan^2a)
=-(sin^2a*tan^2a)^2

(sin^2a-tan^2a)(1-cos^2a)tan^2a
=(sin^2a-tan^2a)(tan^2a-sin^2a)
=-(sin^2a-tan^2a)^2