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Suppose that for some angles xa n dy , t...

Suppose that for some angles `xa n dy ,` the equations `sin^2x+cos^2y=(3a)/2a n dcos^2x+sin^2y=(a^2)/2` hold simultaneously. the possible value of `a` is ___________

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The correct Answer is:
1
`sin^2x+cos^2y=(3a)/2 ...(i)`
`andcos^2x+sin^2y =a^2/2 ...(ii)`
Adding (i) and (ii), we get
`2=(3a)/2 +a^2/2`
`or a^2+3a-4=0`
`or (a+4)(a-1)=0`
`:. A=-4("rehected"),a=1`
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