Question

Question #04cb2

Answer 1

I hope that this helps.

Explanation:

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.