Fez
Lv 4
Fez asked in Science & MathematicsMathematics · 6 years ago

How can I prove that the LHS=RHS ?

Show that (1-Sinx)/cosx = Cox/(1+Sinx)

TRIGONOMETRY

2 Answers

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  • 6 years ago
    Best Answer

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

    work on LHS...

    multiply numerator and denominator by (1 + sin x)/(1 + sin x) [which is equal to ONE !]

    [(1 - sin x)(1 + sin x)]/[cos x(1 + sin x)] = [1 - sin^2 x] / [cos x(1 + sin x)]

    1 - sin^2 x = cos^2 x

    so...

    (cos^2 x)/[cos x(1 + sin x)] = (cos x) / (1 + sin x) RHS

    QED

  • JOS J
    Lv 7
    6 years ago

    (1 - Sin[x])/Cos[x] = Cos[x]/(1 + Sin[x])

    -Sec[x] (-1 + Sin[x]) = Cos[x]/(1 + Sin[x])

    Sec[x] (1 - Sin[x]) (1 + Sin[x]) = Cos[x]

    Sec[x] (1 - Sin[x]^2) = Cos[x]

    Cos[x] = Cos[x]

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