# 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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