trig
posted by Anonymous on .
Prove that if Sinx=5/13 and Siny=12/13, where x and y angles in Q1, then Sin(x+y)=1

sin ( x ) = 5 / 12
cos ( x ) = + OR  sqrt [ 1  sin ^ 2 ( x ) ]
cos ( x ) = + OR  sqrt [ 1  ( 5 / 1 3 ) ^ 2 ]
cos ( x ) = + OR  sqrt ( 1  25 / 169 )
cos ( x ) = + OR  sqrt ( 169 / 169  25 / 169 )
cos ( x ) = + OR  sqrt ( 144 / 169 )
cos ( x ) = + OR  12 / 13
In quaqdrant I cosine are positive so
cos ( x ) = 12 / 13
sin ( y ) = 12 / 13
cos ( y ) = + OR  sqrt [ 1  sin ^ 2 ( y ) ]
cos ( y ) = + OR  sqrt [ 1  ( 12 / 1 3 ) ^ 2 ]
cos ( y ) = + OR  sqrt ( 1  144 / 169 )
cos ( y ) = + OR  sqrt ( 169 / 169  144 / 169 )
cos ( y ) = + OR  sqrt ( 25 / 169 )
cos ( y ) = + OR  5 / 13
In quaqdrant I cosine are positive so
cos ( y ) = 5 / 13
sin ( x + y ) = sin ( x ) * cos ( y ) + cos ( x ) * sin ( y )
sin ( x + y ) = ( 5 / 13 ) * ( 5 / 13 ) + ( 12 / 13 ) * ( 12 / 13 )
sin ( x + y ) = 25 / 169 + 144 / 169
sin ( x + y ) = 169 / 169 = 1