Proving identity

(sinx+tanx)/(cosx+1)=tanx
RS: (sinx+(sinx/cosx))/(cosx+1)
((sinxcosx/cosx)+(sinx/cosx))x 1/(cosx+1)
sinx(cosx+1)/cosx x 1/(cosx+1)
sinx/cosx = tanx
RS = LS

How did sinxcosx/cosx turn to sinx(cosx+1)?

solved

To understand how (sinx*cosx)/cosx turned into sinx(cosx+1), we can simplify the expression step by step:

1. We start with (sinx*cosx)/cosx.

2. We can simplify (cosx/cosx) as it equals 1. So the expression becomes sinx*1.

3. Multiplying sinx by 1 gives us sinx.

Therefore, (sinx*cosx)/cosx simplifies to sinx.

Now, let's look at how sinxcosx/cosx becomes sinx(cosx+1):

1. We begin with sinxcosx/cosx.

2. We can rewrite cosx/cosx as 1. Therefore, the expression becomes sinxcosx*1.

3. Multiplying sinxcosx by 1 gives us sinxcosx.

Therefore, sinxcosx/cosx simplifies to sinxcosx.

It's important to note that sinx(cosx+1) is the expanded form of sinxcosx and both expressions are equivalent.