Thread: Prove the addition problem of cos.

How do you prove the addition formula for cos?

Originally Posted by Swamifez

How do you prove the addition formula for cos?

Which level are you on?
High school or college?
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If college.
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Then,
exp (ix)=cos x+i*sin x
exp (-ix)=cos x-i*sin x

Add,
exp(ix)+exp(-ix) =2cos x
Thus,
cos x=(exp(ix)+exp(-ix))/2=cosh (ix)

Substract,
exp(ix)-exp(ix)=2i*sin x
Thus,
sin x=(exp(ix)+exp(-ix))/2i=-i*sinh (ix)

Thus when you want to show,
cos(x+y)=cos x*sin y+sin x*cos y
Just substitute those identities into the equation and show the left and right hands match