Verify the identity. ( 1-sin x)/cosx=cosx/(1+sin x)

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Question:

Verify the identity. ( 1-sin x)/cosx=cosx/(1+sin x)

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Answer:See below.Step-by-step explanation:I'm going to use what I assume is the correct question.[tex] \dfrac{1 - \sin x}{\cos x} = \dfrac{\cos x}{1 + \sin x} [/tex][tex] \dfrac{\cos x}{\cos x} \times \dfrac{1 - \sin x}{\cos x} = \dfrac{\cos x}{1 + \sin x} [/tex][tex] \dfrac{\cos x(1 - \sin x)}{\cos^2 x} = \dfrac{\cos x}{1 + \sin x} [/tex]Now use the identity [tex] sin^2 x + cos^2 x = 1 [/tex][tex] cos^2 x = 1 - sin^2 x [/tex]We replace [tex] \cos^2 x [/tex] in the left denominator.[tex] \dfrac{\cos x(1 - \sin x)}{1 - \sin^2 x} = \dfrac{\cos x}{1 + \sin x} [/tex]Factor the difference of squares in the left side denominator.[tex] \dfrac{\cos x(1 - \sin x)}{(1 + \sin x)(1 - \sin x)} = \dfrac{\cos x}{1 + \sin x} [/tex][tex] \dfrac{\cos x}{1 + \sin x} = \dfrac{\cos x}{1 + \sin x} [/tex]

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