当x≠kπ/2(k∈Z)时,sinx+tanx/cosx+cotx的值?原式=(sinx+sinx/cosx)/(cosx+cosx/sinx)上下同乘sinxcosx=(sin²xcosx+sin²x)/(cos²xsinx+cos²x)=(sin²x/cos²x)(cosx+1)/(sinx+1)x≠kπ/2sin²x>0,cos²x>0且sin
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![当x≠kπ/2(k∈Z)时,sinx+tanx/cosx+cotx的值?原式=(sinx+sinx/cosx)/(cosx+cosx/sinx)上下同乘sinxcosx=(sin²xcosx+sin²x)/(cos²xsinx+cos²x)=(sin²x/cos²x)(cosx+1)/(sinx+1)x≠kπ/2sin²x>0,cos²x>0且sin](/uploads/image/z/9448154-26-4.jpg?t=%E5%BD%93x%E2%89%A0k%CF%80%2F2%EF%BC%88k%E2%88%88Z%EF%BC%89%E6%97%B6%2Csinx%2Btanx%2Fcosx%2Bcotx%E7%9A%84%E5%80%BC%3F%E5%8E%9F%E5%BC%8F%3D%28sinx%2Bsinx%2Fcosx%29%2F%28cosx%2Bcosx%2Fsinx%29%E4%B8%8A%E4%B8%8B%E5%90%8C%E4%B9%98sinxcosx%3D%28sin%26%23178%3Bxcosx%2Bsin%26%23178%3Bx%29%2F%28cos%26%23178%3Bxsinx%2Bcos%26%23178%3Bx%29%3D%28sin%26%23178%3Bx%2Fcos%26%23178%3Bx%29%28cosx%2B1%29%2F%28sinx%2B1%29x%E2%89%A0k%CF%80%2F2sin%26%23178%3Bx%3E0%2Ccos%26%23178%3Bx%3E0%E4%B8%94sin)
当x≠kπ/2(k∈Z)时,sinx+tanx/cosx+cotx的值?原式=(sinx+sinx/cosx)/(cosx+cosx/sinx)上下同乘sinxcosx=(sin²xcosx+sin²x)/(cos²xsinx+cos²x)=(sin²x/cos²x)(cosx+1)/(sinx+1)x≠kπ/2sin²x>0,cos²x>0且sin
当x≠kπ/2(k∈Z)时,sinx+tanx/cosx+cotx的值?
原式=(sinx+sinx/cosx)/(cosx+cosx/sinx)
上下同乘sinxcosx
=(sin²xcosx+sin²x)/(cos²xsinx+cos²x)
=(sin²x/cos²x)(cosx+1)/(sinx+1)
x≠kπ/2
sin²x>0,cos²x>0
且sinx>-1,cosx>-1
所以cosx+1>0,sinx+1>0
所以恒为正值
请问为什么sinx>-1,cosx>-1?
当x≠kπ/2(k∈Z)时,sinx+tanx/cosx+cotx的值?原式=(sinx+sinx/cosx)/(cosx+cosx/sinx)上下同乘sinxcosx=(sin²xcosx+sin²x)/(cos²xsinx+cos²x)=(sin²x/cos²x)(cosx+1)/(sinx+1)x≠kπ/2sin²x>0,cos²x>0且sin
正弦和余弦的值域就是[﹣1,1]
∵当x≠kπ/2(k∈Z)
∴﹣1取不到
∴只能>﹣1
x∈R时 y=sinx值域 【-1,1】
x≠kπ/2 时 y=sinx值域 (-1,0)∪(0,1) 所以 -1
x≠kπ/2 时 y=cosx值域 (-1,0)∪(0,1) 所以 -1