Proving Trigonometric Identities

[Baron]

When proving trigonometric identities, is it acceptable to simplify both sides of the identity to make both sides meet? Or do you have to work on one side and make it look like the other?

For example, for the identity: tan x / sin x = sec x

Is it okay to prove it like this:
tan x / sin x = sec x
(sin x/ cos x) / sin x = 1/ cos x
(sin x / (cos x * sin x) = 1 / cos x
1 / cos x = 1 / cos x
LHS = RHS

Or do I have to prove it like this
tan x / sin x = sec x
tan x / sin x
sin x / cos x * 1 / sin x
1/ cos x
sec x
LHS = RHS

 

[Deleted member 4993]

When proving trigonometric identities, is it acceptable to simplify both sides of the identity to make both sides meet? Or do you have to work on one side and make it look like the other?

For example, for the identity: tan x / sin x = sec x

Is it okay to prove it like this:
tan x / sin x = sec x
(sin x/ cos x) / sin x = 1/ cos x
(sin x / (cos x * sin x) = 1 / cos x
1 / cos x = 1 / cos x
LHS = RHS

Or do I have to prove it like this
tan x / sin x = sec x
tan x / sin x
sin x / cos x * 1 / sin x
1/ cos x
sec x
LHS = RHS

You should NOT use the RHS as you are working with LHS. SO your work should work as follows:

tan x / sin x

= (sin x/ cos x) / sin x

= (sin x / (cos x * sin x)

= 1 / cos x

= sec(x) = RHS
LHS = RHS