3/(sin20)^2-1/(cos20)^2+64(sin20)^2等于多少?答案是32.请有详细的过程.谢谢

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3/(sin20)^2-1/(cos20)^2+64(sin20)^2等于多少?答案是32.请有详细的过程.谢谢
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3/(sin20)^2-1/(cos20)^2+64(sin20)^2等于多少?答案是32.请有详细的过程.谢谢
3/(sin20)^2-1/(cos20)^2+64(sin20)^2等于多少?
答案是32.请有详细的过程.谢谢

3/(sin20)^2-1/(cos20)^2+64(sin20)^2等于多少?答案是32.请有详细的过程.谢谢
3/(sin20)^2-1/(cos20)^2+64(sin20)^2
=[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