Cosx/(1+sinx) = (1-sinx)/cosx verify this identity

calculate the left side:

cos x / (1+ sin x)

 multiply by (1- sinx/1-sinx)

 to get

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

simplify the numerator than the denominator to get

cosx - cosx sinx / 1-sin^2x

 apply Pythagorean identity to get

 cos x - cosx sin x / cos^2 x

 which simplifies to

1-sinx/cos x which equal the right side so it is true

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step-by-step explanation:

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