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dai so

chung minh dang thuc
(1+Sin2x)/Cos2x=Tan(pi/4+x)

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le

  1. 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

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    Reiny

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