If `sin^2(theta-alpha)c osalpha=cos^2(theta-alpha)sinalpha=msinalphacosalpha,` then prove that `|m|geq1/(sqrt(2))`

Explanation

`sin^(2)(theta-alpha)cos alpha=cos^(2)(theta-alpha)sin alpha=m sin alpha cos alpha`
or `sin^(2)(theta-alpha)=m sin alpha`
`cos^(2)(theta-alpha)=m cos alpha`
Adding, we get
`1=m(sin alpha+cos alpha)`
or `sin alpha+cos alpha=(1)/(m)`
or `sin (alpha+(pi)/(4))=(1)sqrt(2m)`
since `|sin(alpha+(pi)/(4))|le1`
`therefore |(1)/(m(sqrt(2)))|le1` or `|m|ge(1)/sqrt(2)`