Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

how to prove cos x/sin x + sin x/cos x =2/sin2x?

i need help to prove this..

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  • 1 decade ago
    Favorite Answer

    Pf:

    cosx / sinx + sinx / cosx

    =cosx*cosx / sinx*cosx + sinx*sinx / cosx*sinx

    =cos^2(x) / sinxcosx + sin^2(x) / cosxsinx

    =cos^2(x) / sinxcosx + sin^2(x) / sinxcosx

    =(cos^2(x) + sin^2(x)) / sinxcosx

    =1 / sinxcosx

    =2 / 2sinxcosx

    =2 / sin2x

    So cosx/sin x + sinx/cos x =2/sin2x

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  • 1 decade ago

    cosx/sinx +sinx/cosx = (cos^2x+sin^2x)/sinxcosx = 1/sinx.cosx

    = 2/2sinxcosx = 2/sin2x

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  • 1 decade ago

    cosx . . sinx . . .cos²x + sin²x . . . . .1 . . . . . . . . . . 1

    -------- + ------- = -------------------- = -------------- = -------------------- =

    sinx . . .cosx . . . sinxcosx . . . . sinxcosx . . (2sinxcosx)/2

    . . . . 2 . . . . . . 2

    --------------- = ---------

    2sinxcosx . . sin2x

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