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

[Quinn Morris]

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?

 

[dynamicsolo]

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?

 

[Quinn Morris]

so times buy a form of one... 1 over cosacosb?

 

[rock.freak667]

yes that is correct, divide the numerator and denominator by cosacosb