(sinx-2cos)/(sinx+3cosx)=2 求sinxcosx
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(sinx-2cos)/(sinx+3cosx)=2 求sinxcosx
![(sinx-2cos)/(sinx+3cosx)=2 求sinxcosx](/uploads/image/z/19004043-3-3.jpg?t=%28sinx-2cos%29%2F%28sinx%2B3cosx%29%3D2+%E6%B1%82sinxcosx)
万能公式为:设 tan X = Y,则 sin(2X) = 2Y/(1+Y^2)
(sinx-2cosx)/(sinx+3cosx)=2
对于左端,分子\分母同时除以 cosx
(tanx -2)/(tanx + 3) = 2
tanx -2 = 2(tanx + 3)
tanx = -8
sinx*cosx = (1/2) * sin(2x) = (1/2) * 2*tanx/(1 + tan^2 x)
= tanx / ( 1 + tan^2 x)
= -8 /( 1 +64)
= -8/65
(sinx-2cosx)/(sinx+3cosx)=2
对于左端,分子\分母同时除以 cosx
(tanx -2)/(tanx + 3) = 2
tanx -2 = 2(tanx + 3)
tanx = -8
sinx*cosx = (1/2) * sin(2x) = (1/2) * 2*tanx/(1 + tan^2 x)
= tanx / ( 1 + tan^2 x)
= -8 /( 1 +64)
= -8/65
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