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solve the system sinx+cosy=1 cos2x-cos2y=1

solve the system


 


sinx+cosy=1


 


cos2x-cos2y=1

Grade:

2 Answers

vikas askiitian expert
509 Points
10 years ago

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)

lits goyal
31 Points
10 years ago

sinx=.5

cosy=.5

 use cos2x=2cos squarex -1 and eliminate cos x.

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