4=0

Geometry Level 3

I present you my attempt to demonstrate that \(4=0\):

1) Beginning with the well-known identity \(\cos ^{ 2 }{ x } =1-\sin ^{ 2 }{ x } \)

2) \(\cos { x } ={ (1-\sin ^{ 2 }{ x } ) }^{ 1/2 }\)

3) \(1+\cos { x } =1+{ (1-\sin ^{ 2 }{ x } ) }^{ 1/2 }\)

4) \({ (1+\cos { x } ) }^{ 2 }={ (1+{ (1-\sin ^{ 2 }{ x } ) }^{ 1/2 }) }^{ 2 }\)

5) Evaluate \(x=\pi \): \({ (1+\cos { \pi } ) }^{ 2 }={ (1+{ (1-\sin ^{ 2 }{ \pi } ) }^{ 1/2 }) }^{ 2 }\)

6) \({ (1-1) }^{ 2 }={ (1+{ (1-0) }^{ 1/2 }) }^{ 2 }\)

7) \(0=4\)

In which step is the first error committed?

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