If `A={x|cosxgt-(1)/(2)and0lexlepi}andB={x|sinxgt(1)/(2)and(pi)/(3)lexlepi}and" if "pilambdaleAnnBltpimu`, the value of `(lambda + mu)` is

Answer

1

Explanation

`therefore cosxgt-(1)/(2) and 0lexlepi`
`implies-(2pi)/(3)ltxlt(2pi)/(3)and0lexlepi`
`implies0lexlt(2pi)/(3)`
`therefore A = [0, (2pi)/(3)]`
Again, `sinxgt(1)/(2)and(pi)/(3)lexlepi`
`implies (pi)/(3)lexlt(5pi)/(6)`
`B=[(pi)/(3),(5pi)/(6))`
Now, `AnnB=[(pi)/(3),(2pi)/(3))`
`(pi)/(3)leAnnBlt(2pi)/(3)`
Here `lambda=(1)/(3)andmu=(2)/(3)`
`lambda+mu=1`