• Got a question on how to use our new website? Check out our user guide here!

Trig Proof - Help Please (1 Viewer)

Heresy

Member
Joined
Nov 13, 2017
Messages
103
Gender
Male
HSC
2019
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....:spin:
 

fluffchuck

Active Member
Joined
Apr 29, 2016
Messages
242
Location
Sydney
Gender
Male
HSC
2017
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

Member
Joined
Nov 13, 2017
Messages
103
Gender
Male
HSC
2019
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!
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top