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24 November, 06:39

Prove the following trigonometric identities (secx+tanx) (1-sinx/cosx) = 1

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  1. 24 November, 06:53
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    Below.

    Step-by-step explanation:

    Convert to sin's and cos's:-

    (secx + tanx) (1-sinx) / cosx)

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

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

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

    But 1 - sin^2 x = cos^2 x

    so we have

    cos^2 x / cos^2 x which = 1.
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