Question #04cb2

Question

1127 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-07T17:55:48

I hope that this helps.

Prove: $(sin(x)-cos(x))/(sin(x)+cos(x)) = (tan(x)-1)/(tan(x)+1)$

Multiply the left side by 1 in the form of $(1/cos(x))/(1/cos(x))$

$(sin(x)-cos(x))/(sin(x)+cos(x))(1/cos(x))/(1/cos(x)) = (tan(x)-1)/(tan(x)+1)$

Distribute $1/cos(x)$ through the numerator and the denominator:

$(sin(x)/cos(x)-cos(x)/cos(x))/(sin(x)/cos(x)+cos(x)/cos(x)) = (tan(x)-1)/(tan(x)+1)$

Substitute $tan(x)$ for $sin(x)/cos(x)$ and 1 for $cos(x)/cos(x)$

$(tan(x)-1)/(tan(x)+1) = (tan(x)-1)/(tan(x)+1)$

Q.E.D.