is my work correct ?
here is the problem:
tan(arccos(-1/2)+arccos(2/3))
let A=arccos(-1/2)
let A=arccos(2/3)
tan(A+A)=tan(2A)
tan(2A)=2tanA/1-tan^2A
=2(-√3)/(1-(-√3)^2
=-2√3/1+3
=-2√3/4
=-√3/2

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you can't call two different things the same variable and then add them like they are the same.

there is an identity for tan(A+B) though

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