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16 June, 08:20

Verify the identity

cosx/1+sinx + 1+sin/cosx = 2sec x

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  1. 16 June, 08:26
    0
    Ill assume its the first one.

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

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

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

    = 1 + 1 + 2sinx / cos x (1 + sin x) (because sin^2x + cos^2 x = 1)

    = 2 (1 + sin x) / cos x (1 + sin x) = 2 / cos x = 2 sec x
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