Previous page : Euler's identity

We have that

If we instead have minus *θ* as the input we get

If we now add the two equations we get

or

If we subtract the equations instead we get

or

These two formulas for the sine and the cosine will be helpful in some calculus problems. We may, for example, take the derivative of say sin(*θ*) to get

Just as we know it should be. It is not a derivation of the derivative of sin(θ), since we used the derivative of sin(*θ*) to find Euler’s identity – so it is a bit of circular reasoning.

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