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Trigonometry

Verify the identity algebraically.

TAN X + COT Y/TAN X COT Y= TAN Y + COT X

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  1. Rewrite it as

    (tanx + coty)/(tanx coty) = tany + cotx

    LS = (sinx/cox + cosy/siny)/((sinx/cosx)(cosy/siny))
    = [(sinxsiny + cosxcosy)/(cosxsiny) ] / [(sinxcosy)/(cosxsiny) ]
    = (sinxsiny + cosxcosy)/(sinxcoy) (after multiplying by the reciprocal)
    = sinxsiny/(sinxcosy) + cosycosx/)sinxcosy)
    =siny/cosy + cosx/sinx
    = tany + cotx
    = RS

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