Asked by le
chung minh dang thuc
(1+Sin2x)/Cos2x=Tan(pi/4+x)
(1+Sin2x)/Cos2x=Tan(pi/4+x)
Answers
Answered by
Reiny
I assume you want to prove that it is an identity.
LS = (sin^2 x + cos^2 x + 2sinxcosx)/(cos^2 x - sin^2 x)
= (sinx + cosx)^2 / )(cosx+sinx)(cosx-sinx))
= (sinx + cosx)/(cosx - sinx)
RS = (tan π/4 + tanx)/( 1 - (tan π/4)(tanx) )
= (1 + tanx)/(1 - tanx)
= (1 + sinx/cosx) / 1 - sinx/cosx)
multiply top and bottom by cosx
= (cosx + sinx)/(cosx - sinx)
= LS
thus it is proven
LS = (sin^2 x + cos^2 x + 2sinxcosx)/(cos^2 x - sin^2 x)
= (sinx + cosx)^2 / )(cosx+sinx)(cosx-sinx))
= (sinx + cosx)/(cosx - sinx)
RS = (tan π/4 + tanx)/( 1 - (tan π/4)(tanx) )
= (1 + tanx)/(1 - tanx)
= (1 + sinx/cosx) / 1 - sinx/cosx)
multiply top and bottom by cosx
= (cosx + sinx)/(cosx - sinx)
= LS
thus it is proven
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