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