Why do you think it is usually preferable to start with the

Why do you think it is usually preferable to start with the side containing the more complicated expression when establishing a trigonometric identity?

Solution

1. Human brains are accustomed to simplify complicated things rather than complicating a simpler one.

2. A simpler/simplest conclusion of a complicated problem in trigonometric identities is only a handful;mere 2 or 3.

But if I want to complicate a simpler side, outcomes are numerous.

For eg: prove cosx*tanx =sinx

Now I know that if I want to simplify LHS, I will try to convert it is terms of Sin or Cos (which we consider simple in the world of trigonometry)

So cosx*(sinx/cosx)= cosx which is RHS.

But if I want to complicate sinx ,I can write it as

1/cscx or 1-cos^2x or (1-cos2x)/2 . . . . And the list goes on!

So, by and large, it is customary simplify complicated things rather than the other way.

Hope it clarifies your doubt!