How to Prove tan(a - b) = tana - tanb without using a prefix?

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Quinn Morris
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Homework Statement



Prove that: tan (a - b) = tana - tanb
1 + tanatanb​
]​

Homework Equations



cos (a- b) = cosacosb + sinasinb


sin (a - b) = sinacosb - cosasinb


The Attempt at a Solution



I have plugged in the two equations give above since tan - sin/cos and then I'm am stumped of how to proceed

tan (a - b) = sinacosb - cosasinb
cosacosb + sinasinb​

can anyone help please?
 

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Quinn Morris said:
tan (a - b) = sinacosb - cosasinb
cosacosb + sinasinb​

The formula you are trying to arrive at provides the clue: what could you divide numerator and denominator by to get that "1" in the denominator?
 
so times buy a form of one... 1 over cosacosb?