1.

If `x , y in R ,`then the determinant `=|cosx-sinx1sinxcosx1cos(x+y)-sin(x+y)0|`lies in the interval`[-sqrt(2),sqrt(2)]`(b) `[-1,1]``[-sqrt(2),1]`(d) `[-1,-sqrt(2)]`

Answer» `|(cos x , -sin x,1),(sin x, cos x,1),(cos(x+y), -sin(x+y), 0)|`
`|(cos x, -sin x,1),(sin x, cos x,1),(cos x cos y - sin xsiny , -sinxcosy - cosx siny , 0)|`
`r_3 -> r_3 - cosy(r_1) + siny(r_2)`
`|(cosx, - sinx,1),(sin x, cos x,1),(0,0, siny - cosy)|`
`(sin y - cos y)[cos^2 x - (-sin^2x)]`
`= (siny - cos y)(cos^2x+sin^2 x)`
`= siny - cosy`
`= -[cosy - siny]`
`= - sqrt2[ 1/sqrt2 cos y - 1/sqrt2 sin y]`
`- sqrt2 sin(pi/4 - y)`
when it is `=1`
`/_= - sqrt2`
when it is `= -1`
`/_ = sqrt2`
a is correct option


Discussion

No Comment Found

Related InterviewSolutions