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solve the system sinx+cosy=1 cos2x-cos2y=1
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)
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.
sinx=.5
cosy=.5
use cos2x=2cos squarex -1 and eliminate cos x.
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