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If A=[(costheta,-sintheta),(sintheta,cos...

If `A=[(costheta,-sintheta),(sintheta,costheta)]` find the values of `theta` satisfying the equation `A^(T)+A =" "I _(2).`

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we have, `A^(T) " " A " " I_(2)` lt brgt `rArrA[(cos0,sin0),(-sin0,cos0)]+[(cos0,-sin0),(sin0,cos0)]=[(1,0),(0,1)]`
`rArr[(2cos0,0),(0,2cos0)]=[(1,0),(0,1)]`
`rArr cos0 = (1)/(2) = cos((pi)/(3)) rArr 0 = 2npipm (pi)/(3), n in`
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