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  • f(x)=cos2x/sin(x+π/4) 若f(x)=4/3,求sin2x的值

    f(x)=cos2x/sin(x+π/4) 若f(x)=4/3,求sin2x的值
    數(shù)學(xué)人氣:334 ℃時(shí)間:2020-02-05 21:32:27
    優(yōu)質(zhì)解答
    cos2x/sin(x+π/4) =4/3
    cos2x/sin(x+π/4) =4/3
    (cos² x-sin² x)/sin(x+π/4) =4/3
    (cosx-sinx)(cosx+sinx)/sin(x+π/4) =4/3
    (cosx-sinx)[√2(√2/2cosx+√2/2sinx)]/sin(x+π/4) =4/3
    (cosx-sinx)[√2(sinπ/4cosx+cosπ/4sinx)]/sin(x+π/4) =4/3
    (cosx-sinx)[√2sin(x+π/4)]/sin(x+π/4) =4/3
    √2(cosx-sinx)=4/3(平方)
    2(cosx-sinx)²=16/9
    (cosx-sinx)²=8/9
    cos²x+sin²x-2sinxcosx=8/9
    1-2sinxcosx=8/9
    2sinxcosx=1/9
    sin2x=1/9
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