1.

If sinx=(1)/(sqrt(5)),siny=(1)/(sqrt(10))" where "0ltxlt(pi)/(2),0ltylt(pi)/(2),then what is (x+y) equal to ?

Answer»

`pi`
`(pi)/(2)`
`(pi)/(4)`
0

Solution :`SINX=(1)/(sqrt(5)),siny=(1)/(sqrt(10)),0ltxlt(pi)/(2),0ltylt(pi)/(2)`
`cosx=sqrt(1-sin^(2)x)"" cosy=sqrt(1-sin^(2)y)`
`=sqrt(1(1)/(5))""=sqrt(1-(1)/(10))`
`=sqrt((4)/(5))=(2)/(sqrt(5)) ""=sqrt((9)/(10))=(3)/(sqrt(10))`.
`sin(x+y)=sinxcosy+cosx siny`
`=(1)/(sqrt(5)).(3)/(sqrt(10))+(2)/(sqrt(5))*(1)/(sqrt(10))`
`=(5)/(sqrt(5)*sqrt(10))=(sqrt(5).sqrt(5))/(sqrt(5).sqrt(10))=sqrt((5)/(10))=sqrt((1)/(2))=(1)/(sqrt(2))`.
`thereforex+y=sin^(-1)((1)/(sqrt(2)))=(pi)/(4)`.


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