Simplify the LHS of the identity?

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

Simplify the LHS of the equation, please provide all steps THANK YOU! :)

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  • cidyah
    Lv 7
    6 years ago
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  • 6 years ago

    L.H.S = tan(x)-sin(x)) / (tan(x)sin(x))

    = [(sinx/cosx) - sinx] / [(sinx/cosx)sinx]

    = [sinx(1 - cosx)/cosx] / [sin²x/cosx]

    = { [sinx(1 - cosx)] / [sin²x] } [cosx/cosx]

    = {(1 - cosx) / [sinx]} (1) = (1 - cosx) / sinx = RHS

    hope this helps

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  • M3
    Lv 7
    6 years ago

    (tanX - sinX) / (tanX.sinX) ...... divide top & bottom by tanX

    = (1 - sinX / tanX) / tanX ........ simplify sinX / tan X

    = (1 - cosX ) / sinX

    QED

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