1.

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

Answer» `sin^2(theta-alpha)cosalpha=msinalphacosalpha`
`sin^2(theta-alpha)=msinalpha-(1)`
`cos^2(theta-alpha)sinalpha=msinalphacosalpha`
`cos^2(theta-alpha)=mcosalpha-(2)`
adding equation 1 and 2
`sin^2(theta-alpha)+cos^2(theta-alpha)=m(sinalpha+cosalpha)`
`1=m(sinalpha+cosalpha)`
`[sinalpha+cosalpha=1/m]1/sqrt2`
`1/sqrt2sinnalpha+1/sqrt2cosalpha=1/(sqrt2m)`
`sin(alpha+pi/4)=1/(sqrt2m)`
`|sinx|<=1`
`|sin(alpha+pi/4)|<=1`
`|1/(sqrt2m)|<=1`
`|1/m|<=sqrt2`
`|m|>=1/sqrt2`.


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