Help me please. How to prove this ? ( \cos(x) + \sin(x) )/( \cos(x ) - \sin(x) ) = \tan(45 + x) ​

Question

Help me please. How to prove this ?


`( \cos(x) + \sin(x) )/( \cos(x ) - \sin(x) ) = \tan(45 + x)`
​

Answer 1

• First, you want to divide the numerator and denominator by the cosine(x), and afterwards, it looks like this...

`(tan~x+1)/(tan~x-1)`

• Include 45 as one of the parameters and correlate with tan.

`(tan~x+tan~45)/(tan~x-tan~45)`

• Next, you want to multiply the numerator and denominator by the conjugate of the denominator, in this case, tan x + tan 45.

• Lastly, simplify, and you have the answer as tan(45 + x)