Can anyone help me verify this identity?

tan (a-b) = (1 - cot(a) tan(b)) / cot(a) + cot(b)

Thank you

Can anyone help me verify this identity?

tan (a-b) = (1 - cot(a) tan(b)) / cot(a) + cot(b)

Thank you

tan (a-b) = (1 - cot(a) tan(b)) / cot(a) + cot(b)

Thank you

I apologize if this is a duplicate post. I thought I posted it already, but I cannot find it anywhere.

Can anyone help me verify the identity below?

tan (a-b) = (1 - cot(a )tan(b)) / cot(a) + tan(b)

Can anyone help me verify the identity below?

tan (a-b) = (1 - cot(a )tan(b)) / cot(a) + tan(b)

- little_dragon
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they show how to do this stuff here: http://www.purplemath.com/modules/proving.htmCan anyone help me verify this identity?

tan (a-b) = (1 - cot(a) tan(b)) / cot(a) + cot(b)

the right hand side (RHS) is messier so try starting there

see if maybe the fraction simplifies

1 - cot(a)tan(b) = 1 - cot(a)/cot(b) = [cot(b) - cot(a)] / cot(b)

then the whole thing is

[cot(b) - cot(a)] / cot(b)

----------------------------

cot(a) + cot(b)

cot(b) - cot(a)

---------------------------

cot(b) [cot(a) + cot(b)]

maybe this isn't going anywhere?

what happens if we turn this into tangents?

1/tan(b) - 1/tan(a)

-----------------------------

[1/tan(b)] [1/tan(a) + 1/tan(b)]

[tan(a) - tan(b)] / [tan(b)tan(a)]

---------------------------------------

[1/tan(b)] [{tan(b) + tan(a)} / tan(b)tan(a)]

move stuff around

[tan(a) - tan(b)} / [tan(a)]

---------------------------------------

[{tan(b) + tan(a)} / tan(b)tan(a)]

tan(a) - tan(b)

------------------------------

[tan(b) + tan(a)] / tan(b)

tan(a) - tan(b)

--------------------

1 + tan(a)/tan(b)

this is close to the right identity but not quite

is that one tangent in the original maybe supposed to be a cotangent?

thanks