The Student Room Group
Reply 1
23) cosy = sin (x+y)
cosy = sinxcosy + sinycosx
divide by cosy:
1 = sinx + cosxtany
divide by cosx
secx = tanx + tany
tany = secx - tanx Q.E.D.
turtle2
Could somebody please help me with these questions:

From C3 book, ex. 7A
18) Given that 3sin(x-y)-sin(x+y)=0, show that tanx=2tany.
b) Solve 3sin(x-45)-sin(x+45)=0 for 0<=&#952;<=360.

19) Given that sinx(cosy+2siny)=cosx(2cosy-siny), find the value of tan(x+y).

23) Given that cosy=sin(x+y), show than tany=secx-tanx.


18) 3sin(x-y)-sin(x+y)=0
3sinxcoy-3sinycosx-sinxcosy-cosxsiny=0
2sinxcosy-4sinycosx=0
sinxcosy=2sinycosx
sinx=2tanycosx
tanx=2tany
b) use part a with y=45
19)
sinx(cosy+2siny)=cosx(2cosy-siny)
sinxcosy+2sinysinx=2cosxcosy-cosxsiny
sinxcosy+cosxsiny=2(cosxcosy-sinxsiny)
sin(x+y)=2cos(x+y)
tan(x+y)=2

20) cosy=sin(x+y)
=sinxcosy+cosxsiny
1=sinx+cosxytany
1-sinx=cosxtany
secx-tanx=tany
Reply 3
18) Given that 3sin(x-y)-sin(x+y)=0, show that tanx=2tany.
b) Solve 3sin(x-45)-sin(x+45)=0 for 0<=&#952;<=360.

a) 3sin(x-y) - sin(x+y) = 0
3[sinxcosy - sinycosx] - [sinxcosy + sinycosx] = 0
3sinxcosy - 3sinycosx - sinxcosy - sinycosx = 0
2sinxcosy - 4sinycosx = 0
sinxcosy - 2sinycosx = 0
sinxcosy = 2sinycosx
divide by cosy
sinx = 2tanycosx
tanx = 2tany [where cosx and cosy dont equal zero ]

b) 3sin(x-45)-sin(x+45)=0
then substitute y = 45 in tanx = 2tany
then solve to find x
Reply 4
thanks a lot!