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solve the system
sinx+cosy=1
cos2x-cos2y=1
cos2x = 1-2sin2x ......1
cos2y = 2cos2y-1 .........2
we have , cos2x-cos2y = 1
so , after putting 1 & 2 in above eq we get
2(sin2x + cos2y) = 1
sin2x+cos2y = 1/2 ...............3
sinx+cosy = 1 .......................4 (given)
now ,
(sinx+cosy)2 = sin2x + cos2x + 2sinxcosy
12 = 1/2 + 2sinxcosy
sinxcosy = 1/4 ................5
now from 4 & 5
sinx(1-sinx) = 1/4
(2sinx-1)2 = 0
sinx= 1/2 cosy = 1/2
x = npi +(-1)n (pi/6) y = 2npi +(-) (pi/3)
sinx=.5
cosy=.5
use cos2x=2cos squarex -1 and eliminate cos x.
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