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If A=[(cosx,sinx),(-sinx,cosx)] , find x...

If `A=[(cosx,sinx),(-sinx,cosx)]` , find `x` satisfying `0`<`x`<`pi/2` when `A+A^T=I`

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Given: `A=[(cosx,sinx),(-sinx,cosx)]`
Then,
`A^T=[(cosx,sinx),(-sinx,cosx)]^T`
`A^T=[(cosx,-sinx),(sinx,cosx)]`
When `A+A^T=I`
`implies [(cosx,sinx),(-sinx,cosx)]+[(cosx,-sinx),(sinx,cosx)]=[(1,0),(0,1)]`
`implies [(cosx+cosx,sinx-sinx),(-sinx+sinx,cosx+cosx)]=[(1,0),(0,1)]`
`implies [(2cosx,0),(0,2cosx)]=[(1,0),(0,1)]`
...
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