作业帮求值:3/(sin^2 20°)-1/(cos^2 20°)+64sin^2 20°
来源：学生作业帮助网 编辑：作业帮 时间：2024/07/11 13:46:33
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求值:3/(sin^2 20°)-1/(cos^2 20°)+64sin^2 20°
求值:3/(sin^2 20°)-1/(cos^2 20°)+64sin^2 20°
求值:3/(sin^2 20°)-1/(cos^2 20°)+64sin^2 20°
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