Trig Proof - Help Please (1 Viewer)

[Heresy]

Question:

Given that 0 < x < Pi/4, prove that tan(Pi/4 + x) = cosx + sinx/cosx - sinx

I got this problem for homework on the leadup to an exam coming up in 3 weeks - someone help please?

P.S. Im sorry that I don't know how type Pi....

 

[fluffchuck]

tan(pi/4 + x)
= (tan(pi/4) + tan(x))/(1 - tan(pi/4)tan(x)) (tan expansion formula)
= (1 + tan(x))/(1 - tan(x))
= (cos(x) + tan(x)cos(x))/(cos(x) - tan(x)cos(x)) (multiplying the top and bottom by cos(x))
= (cos(x) + sin(x))/(cos(x) - sin(x))

 

[Heresy]

tan(pi/4 + x)
= (tan(pi/4) + tan(x))/(1 - tan(pi/4)tan(x)) (tan expansion formula)
= (1 + tan(x))/(1 - tan(x))
= (cos(x) + tan(x)cos(x))/(cos(x) - tan(x)cos(x)) (multiplying the top and bottom by cos(x))
= (cos(x) + sin(x))/(cos(x) - sin(x))

Thank you so much!