prove the identity \[\left( \cos x \over 1 +\sin x \right)=\left( 1-\sin x \over \cos x \right)\]

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prove the identity \[\left( \cos x \over 1 +\sin x \right)=\left( 1-\sin x \over \cos x \right)\]

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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LHS/RHS=1
because cos x cos x = 1- sin x sin x
By multiplying the left hand side by 1-sinx, we get \[{\cos{x}(1-\sin{x}) \over 1-\sin^2{x}}={\cos(x)(1-\sin(x) \over \cos^2(x)}={1-\sin{x} \over \cos{x}}\]

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Other answers:

Which is what we have on the right hand side obviously.
that was simple. thanks.
It is simple! :)
Yifan you help me so much! and I really appreciate it, but many of times I don't understand the way you teach.. I am sorry. :S
His argument is not that difficult, he's using that if a=b\(\ne\)0, then a/b=1.
actually i should use LHS-RHS=0 to prove that

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