I found this in my math book. It gives this supposed proof that 0=4 and asks where the error is. Note that this isn't homework. I found it at the end of the unit among other bonus problems to supposedly test ingenuity. Here it is:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]sin^2 \theta + cos^2 \theta = 1 \Rightarrow cos \theta = \sqrt{1-sin^2 \theta}[/itex]

Now we add 1 to both sides and then square them.

[itex]1 + cos \theta = 1 + \sqrt{1-sin^2 \theta}[/itex]

[itex](1 + cos \theta)^2 = (1 + \sqrt{1-sin^2 \theta})^2[/itex]

Next we substitute theta with pi.

[itex](1 + cos \pi)^2 = (1 + \sqrt{1-sin^2 \pi})^2[/itex]

Given that

[itex]cos \pi=-1[/itex]

[itex]sin \pi=0[/itex]

it follows:

[itex](1-1)^2=(1+ \sqrt{1-0^2})^2[/itex]

[itex]0=2^2 \Rightarrow 0=4[/itex]

So, what's the problem here?

Thanks for taking time to read this and hopefully solve it.

Have a nice day.

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# Proof 0=4

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