Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

cosx(tanx+cotx)=cscx Prove?

How do I prove this?

7 Answers

Relevance
  • kb
    Lv 7
    1 decade ago
    Favorite Answer

    cos x (tan x + cot x)

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

    = cos x [(sin^2(x) + cos^2(x)) / (sin x cos x)], common denominator

    = [(sin^2(x) + cos^2(x)) / (sin x)]

    = 1/ sin x

    = csc x.

  • Anonymous
    5 years ago

    multiply cosx with cotx. You get (cos^2)/sin. Make sin into (sin^2)/sin. Add them you get (cos^2+sin^2)/sin. Use your trig properties and you know that (cos^2+sin^2)=1 and 1/sin is csc.

  • Anonymous
    1 decade ago

    LeftHandSide = cosx(sinx/cosx + cosx/sinx)

    = sinx + cosx^2/sinx

    =sinx +(1-sinsx^2)/sinx

    = (sinx^2 + 1 -sinx^2)/sinx

    = 1/sinx = cscx = RightHandSide

    QED

  • 1 decade ago

    =cosx (sinx/cosx + cosx/sinx)

    = sinx + (cosx)^2/ sinx

    = (sinx)^2 / sinx + (cosx)^2/ sinx

    = 1/sinx

    = cscx

  • How do you think about the answers? You can sign in to vote the answer.
  • TomV
    Lv 7
    1 decade ago

    cos(tan + cot) = csc

    cos(sin/cos + cos/sin) = 1/sin

    sincos(sin/cos + cos/sin) = 1

    sin^2 + cos^2 = 1

    1 = 1

  • 1 decade ago

    cos(sin/cos + cos/sin) = 1/sin

    sincos(sin/cos + cos/sin) = 1

    sin^2 + cos^2 = 1

  • Anonymous
    1 decade ago

    CosX(TanX+CotX)=CscX

    CosX(SinX/CosX+CosX/SinX)=CscX

    SinxCosx/Cosx+CosxCosx/Sinx=CscX

    SinX+(1-SinxSinx)/Sinx=CscX

    SinX+1/sinx-Sinx=CscX

    1/SinX=CscX

    CscX=CscX

Still have questions? Get your answers by asking now.