Trig Proving Question

[ninbam1k]

If cos (x+y) = 0, prove that sin(x+2y) = sin (x)

my leads are..

cos ( (x + 2y) - y ) = 0

cos(x+2y)cos(y) + sin(x+2y)sin(y) = 0
 
yeah, kinda stuck here so if you can help me out great

thanks in advance!

[taiga]

split cos(x+2y) into cos(x+y + y)

then try =)

If not I'll work it through

I'm not sure about this, but if cos of something equals 0, then sin of that something should equal 1 or -1 :X

[ninbam1k]

thanks for the hint mate

[JinXi]

Since cos(x+y)=0

cos(x)cos(y)-sin(x)sin(y)=0
cos(x)cos(y)=sin(x)sin(y)

So,

sin(x+2y) =sin((x+y)+y)
             =sin(x+y)cos(y)+cos(x+y)sin(y) , since cos(x+y)=0

sin(x+2y) =sin(x+y)cos(y)
             =[sin(x)cos(y)+cos(x)sin(y)]cos(y)
             =sin(x)cos^2(y)+cos(x)cos(y)sin(y) , since cos(x)cos(y)=sin(x)sin(y)
             =sin(x)cos^2(y)+sin(x)sin^2(y)
             =sin(x)[sin^2(y)+cos^2(y)]
             =sin(x)

1 month of freedom has made my mind soo rusty

[98.40_for_sure]

cos(x+y) = 0
cos(x).cos(y) - sin(x).sin(y) = 0
cos(x).cos(y) = sin(x).sin(y)
sin(x+2y) = sin(x).cos(2y) + sin(2y).cos(x)
= sin(x)[1-2sin^2(y)] + 2sin(y).cos(y).cos(x)
= sin(x) - 2sin(x)sin^2(y) + 2sin(x)sin^2(y)
= sin(x)

EDIT: beaten lol

[ninbam1k]

LOL, hey arent you 99.95_for_sure? LOL

BTW THANKS GUYS ^^

[JinXi]

LOL, hey arent you 99.95_for_sure? LOL

Lol he was, until a fateful catastrophe that occurred on a Monday morning at 7a.m 13th of December 2010.