Verify Trigonometric Identity (1+sec x)/(tan x + sin x)=csc x?

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  • 1 decade ago
    Favorite Answer

    (1+ secx) / (tanx + sinx) = cscx {multiply (tanX + Sinx by both sides to get out of the denominator}

    (1 + Secx) = Csc(TanX + SinX) {you will need to distribute, and break down Csc}

    (1 + SecX) = (1 / SinX)(SinX / CosX) + (1/SinX)(SinX) {multiply out}

    1 + SecX = (Sinx / [(SinX)(CosX)]) + (SinX / SinX)

    1 + SecX = (1 / CosX) + 1

    1 + SecX = 1 + (1 / CosX)

    1 + (1 / CosX) = 1 + (1 / CosX)

    Checks!

  • 1 decade ago

    1+sec(x) = 1 + [1/cos(x)]

    =[cos(x)+1]/cos(x)

    tan x + sin x = (sinx/cosx)+sinx

    =[sinx + sinx.cosx] / cosx

    =sinx[cosx+1] / cosx

    [1+sec(x)] / [tan x + sin x]=1 / sinx

    =csc x

  • Como
    Lv 7
    1 decade ago

    LHS

    ----------

    1 + sec x

    ------------------

    tan x + sin x

    cos x + 1

    ----------------------------

    sin x + cos x sin x

    cos x + 1

    --------------------------

    sin x ( 1 + cos x )

    1

    --------

    sin x

    csc x

    RHS

    --------

    csc x

    LHS = RHS

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