Trig Question - HSC Exam Style 3U (1 Viewer)

TooSleepy

New Member
Joined
Jun 25, 2011
Messages
10
Location
Sydney
Gender
Female
HSC
2013
Not exactly sure where this came from originally but it's on a sheet our teacher gave us :) And....i have no idea how to do it:

Given that 0 < x < π/4 , prove that

tan(π/4 + x) = ( cosx + sinx )/( cosx - sinx )
 

Aesytic

Member
Joined
Jun 19, 2011
Messages
141
Gender
Male
HSC
2012
LHS = tan(pi/4 + x)
= [tan(pi/4) + tanx]/[1-(tan(pi/4)*tanx)]
= [1 + tanx]/[1 - tanx] since tan(pi/4) = 1
= [1 + sinx/cosx]/[1-sinx/cosx]
multiplying top and bottom by cosx,
= [cosx + sinx]/[cosx - sinx]
= RHS
 

TooSleepy

New Member
Joined
Jun 25, 2011
Messages
10
Location
Sydney
Gender
Female
HSC
2013
Ohhh so using the compound angle thing....
i get it! :)
Thanks aesytic!!
 

TooSleepy

New Member
Joined
Jun 25, 2011
Messages
10
Location
Sydney
Gender
Female
HSC
2013
Oh thanks too carrotsticks!
Two ways to do it....hmm, i wonder which one's better.....
both get you the marks though so i guess it doesn't really matter :)
 

ahdil33

Member
Joined
Feb 28, 2011
Messages
183
Gender
Male
HSC
2012
Same thing really isn't it? But I think the first is easier because expanding a compound angle is easier than realising it could be put in the form of one, especially as tan (pi/4) = 1
 

Carrotsticks

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
Oh thanks too carrotsticks!
Two ways to do it....hmm, i wonder which one's better.....
both get you the marks though so i guess it doesn't really matter :)
Well Aeystic proved one direction (baby you light up my world like nobody else) whereas I did another direction, but his one is more intuitive than mine. For some reason I read the question as prove (expression with sin and cos) = (expression with tan) when you in fact had written it the other way around!
 

Sanjeet

Member
Joined
Apr 20, 2011
Messages
239
Gender
Male
HSC
2012
Why do they give you 0 < x < π/4 as a condition if it is not needed in the solution?
 

Sy123

This too shall pass
Joined
Nov 6, 2011
Messages
3,730
Gender
Male
HSC
2013
Why do they give you 0 < x < π/4 as a condition if it is not needed in the solution?
Carrotsticks cancelled out cos x, so in the given domain, he can because cos x =/= in that domain. (I think)

EDIT: I graphed both sides of the equation on Geogebra, and they seem to be the exact same for all values of x, I was guessing that they might of given you that domain, because it was only exactly the same for that domain, (or in the domain similar to it)
 
Last edited:

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

Top