化简3/(sin^220°)-1/(cos^220°)+64sin^220°

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/26 09:00:38
化简3/(sin^220°)-1/(cos^220°)+64sin^220°化简3/(sin^220°)-1/(cos^220°)+64sin^220°化简3/(sin^220°)-1/(cos^22

化简3/(sin^220°)-1/(cos^220°)+64sin^220°
化简3/(sin^220°)-1/(cos^220°)+64sin^220°

化简3/(sin^220°)-1/(cos^220°)+64sin^220°
3/sin^2 20-1/cos^2 20+64sin20
=[3(cos20)^2-(sin20)^2]/(sin20)^2(cos20)^2+64(sin20)^2
=[(√3cos20+sin20)(√3cos20-sin20)]/(sin20cos20)^2+64(sin20)^2
=[2sin(60+20)*2sin(60-20)]/[(sin40)/2]^2+64(sin20)^2
=16sin80sin40/sin40*sin40+64(sin20)^2
=16sin80/sin40+64(sin20)^2
=32sin40cos40/sin40+64(sin20)^2
=32cos40+64(sin20)^2
=32[1-2(sin20)^2]+64(sin20)^2
=32