已知tanx/2=根号5,求(1+sinx-cosx)/(1+sinx+cosx)的值!
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已知tanx/2=根号5,求(1+sinx-cosx)/(1+sinx+cosx)的值!
已知tanx/2=根号5,求(1+sinx-cosx)/(1+sinx+cosx)的值!
已知tanx/2=根号5,求(1+sinx-cosx)/(1+sinx+cosx)的值!
sinx = 2tan(x/2)/(1+tanx/2tanx/2)
= 2*sqrt(5)/(1+5)
= sqrt(5)/3
cosx = (1-tanx/2tanx/2)/(1+tanx/2tanx/2)
= -2/3
(1+sinx-cosx)/(1+sinx+cosx)
= (1+ sqrt(5)/3+2/3)/(1+ sqrt(5)/3-2/3)
= sqrt(5)
注: sqrt(5)为根号5
或者(为表达方便令t=tanx/2)
sina = 2t/(1+t*t)
cosa = (1-t*t)/(1+t*t)
代人有
(1+sinx-cosx)/(1+sinx+cosx) = 2t(t+1)/[2(t+1)]
= t
= tanx/2
= 根号5
(1+sinx-cosx)/(1+sinx+cosx)=(1+2sinx/2cosx/2-1+2sin^2x/2)/(1+2sinx/2cosx/2+2cos^x/2-1)=(2sinx/2cosx/2+2sin^2x/2)/(2sinx/2cosx/2+2cos^x/2)=(tanx/2+tan^2x/2)/(tanx/2+1)=tanx/2=根号5