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18 November, 20:16

Write each expression in terms of sines and/or cosines and then simplify.

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

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  1. 18 November, 20:38
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    Tan (x) = sin (x) / cos (x), therefore, substitute sin (x) / cos (x) in the expression:

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

    simplify the 2 cos (x):

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

    Sin^2 (x) + cos^2 (x) = 1, sin^2 (x) - 1 = - cos^2 (x), substitute in the expression:

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