prove cos(x) / [1 + sin(x)] = [1 - sin(x)] / cos(x)

[NEHA]

Prove the following identity:

. . .cos(x) / [1 + sin(x)] = [1 - sin(x)] / cos(x)

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I did the following:

. . .[cos(x) / cos(x)] * [1 + sin(x)] / cos(x)

. . . . .= [cos(x) (1 + sin(x))] / cos^2(x)

. . . . .= [cos(x) (1 + sin(x))] / [1 - sin^2(x)]

. . . . .= [cos(x) (1 + sin(x))] / [(1 - sin(x))(1 + sin(x))]

. . . . .= cos(x) / [1 - sin(x)]

...by cancelling the common factor of "1 + sin(x)".
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Edited by stapel -- Reason for edit: spelling, subject line, formatting, etc

 

[stapel]

Looks good to me.

Eliz.