Solve Math Trig Identities w/ Sin & Cos Only

[Stanc]

Hi I am in need of some help for this question:

1+tanx/1-tanx = tan(x+(∏/4))

It is easy to solve with the tan trig identites on the right side however, my teacher had told me to do it with SIN and COS only. I am not sure if its possible and was looking for some insight

Left Side:
Cosx+Sinx/Cosx-Sinx


Right Side:
End up with
{(SinxCos∏/4) + (CosxSin∏/4)}/ (CosxCos∏/4) - (SinxSin∏/4)

Can anyone give me some insight?

 

[pasmith]

A good first step is to replace cos($\pi$/4) and sin($\pi$/4) by their actual values.

 

[Stanc]

A good first step is to replace cos($\pi$/4) and sin($\pi$/4) by their actual values.

Yes. I have tried that but then i get stuck at:

(Sinx(√2/2)) + (Cosx(√2/2)) / (Cosx(√2/2)) - (Sinx(√2/2))

IS there anything i can do?

 

[AlephZero]

Don't get confused by all the notation. This is just the same as simplfying something like
$$\frac{3a + 3b}{3c - 3d}$$

 

[Stanc]

Don't get confused by all the notation. This is just the same as simplfying something like
$$\frac{3a + 3b}{3c - 3d}$$

I don't think I am catching it. I understand how to simplify the example you had but i cannot factor out a sin or a cos?

 

[Stanc]

Nevermind, I feel reallydumb... i got it, thanks guys

 

[Mark44]

Hi I am in need of some help for this question:

1+tanx/1-tanx = tan(x+(∏/4))

The left side needs parentheses!

What you wrote is 1 + (tanx)/1 - tanx, which is equal to 1.

What you meant was (1 + tanx)/(1 - tanx).