Question

verify the identity
(1-sinx)/cosx) = (cosx/1+sinx)

Answer 1

multiply the left-hand by 1+sinx

Answer 2

So cosx=cosx?

Answer 3

Keep in mind this is valid ONLY for \(1+\sin(x) \ne 0\).

Answer 4

When you are proving an identity you only work with one side.

Answer 5

I am stuck, how to prove? everybody?

Answer 6

@Luigi0210 @tkhunny

Answer 7

Do I work it out?

Answer 8

not that way, we have to start from valid logic.

Answer 9

@dan815

Answer 10

\[\frac{ 1-sinx }{ cosx }=\frac{ cosx }{ 1+sinx }\]
\[\frac{ 1-sinx }{ cosx }*\frac{ 1+sinx }{ 1+sinx }=\]
\[\frac{ 1-\sin^2x }{ cosx(1+sinx) }=\]
\[\frac{ \cos^2x }{ (cosx)(1+sinx) }=\]
\[\frac{ cosx }{ 1+sinx }=\frac{ cosx }{ 1+sinx }\]

Answer 11

your logic is perfect under the condition which tkhuny indicated above. However, It cannot be used when you don't know whether it's valid or not.

Answer 12

this is a Prove problem, with an invalid logic, I dare not apply.