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Solve the equation `2sinx+cosy=2`for the value of `xa n dydot`

Answer» `2sinx+cosy = 2`
`=>cosy = 2(1-sinx)->(1)`
As `-1 le cosy le 1`
`:. -1 le 2(1-sinx) le 1`
`=> -1/2 le 1-sinx le 1/2`
`=> 1/2 le sinx le 3/2`
As maximum value of `sinx` can be `1`,
`:. 1/2 le sinx le 1`
`:. x in [pi/6,pi/2].`
Now, when `x = pi/6`,
`cosy = 2(1-sin(pi/6)) = 2(1/2) = 1`
`=> y = 0`
Now, when `x = pi/2`,
`cosy = 2(1-sin(pi/2)) = 2(0) = 0`
`=> y = pi/2`
`:. x in [pi/6,pi/2].`
`:. y in [0,pi/2].`


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