(1/cosx) + tanx = (cosx)/(1-sinx). Prove that LHS = RHS. Please help anyone?

2 Answers

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  • 8 years ago
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    LHS = (1 / cos x) + tan x

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

    = (1 + sin x) / cos x

    = [(1 + sin x)(1 − sin x)] / cos x (1 − sin x)

    = (1 − sin² x) / cos x (1 − sin x)

    = cos² x / cos x (1 − sin x)

    = cos x / (1 − sin x)

    = RHS

  • Anonymous
    8 years ago

    L H S

    -------

    1/cos x +tan x

    RHS

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

    cos x (1+sin x) / (1-sin^2 x)

    cos x (1+sin x) / cos^2 x

    = (1+sin x ) / cos x

    = 1 / cos x + sin x / cos x

    1 / cos x + tan x

    = L H S

    so proved.

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