Question

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

Answer 1

LHS/RHS=1

Answer 2

because cos x cos x = 1- sin x sin x

Answer 3

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

Answer 4

Which is what we have on the right hand side obviously.

Answer 5

that was simple. thanks.

Answer 6

It is simple! :)

Answer 7

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

Answer 8

His argument is not that difficult, he's using that if a=b\(\ne\)0, then a/b=1.

Answer 9

actually i should use LHS-RHS=0 to prove that