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(1-cotx+cscx)·(1-tanx+secx)如何解决?
csc sec是什么来的?
人气:332 ℃ 时间:2020-05-22 20:47:26
解答
tanx = sinx/cosx
cotx = cosx/sinx
cscx = 1/sinx
secx = 1/cosx
(1-cotx+cscx)(1-tanx+secx)
=(1-cosx/sinx+1/sinx)(1-sinx/cosx+1/cosx)
=((sinx-cosx+1)/sinx)((cosx-sinx+1)/cosx)
=(1-(sinx-cosx)^2)/(sinxcosx)
=(1-(sinx)^2+2sinxcosx-(cosx)^2)/(sinxcosx)
=2sinxcosx/(sinxcosx)
=2
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