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```        solve the system

sinx+cosy=1

cos2x-cos2y=1```
6 years ago

510 Points
```										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)
```
6 years ago
lits goyal
31 Points
```										sinx=.5
cosy=.5
use cos2x=2cos squarex -1 and eliminate cos x.
```
6 years ago
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