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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<=θ<=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.

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<=θ<=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.

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<=θ<=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.

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<=θ<=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

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<=θ<=360.

b) Solve 3sin(x-45)-sin(x+45)=0 for 0<=θ<=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

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