Sum and Difference Formulas

[monkey12]

Hi, I can't figure out this problem. I used a for alpha, and b for beta.
Verify the identity:

cos(a + b) 1-tan(a)tan(b)
cos(a - b) = 1+tan(a)tan(b)

As far as I got: cos(a)cos(b)-sin(a)sin(b)
cos(a)cos(b)+sin(a)sin(b)
Any help would greatly be appreciated, because I am new to all this Trig identity stuff.

BTW I know that the identity for tan(a + b)= tan(a) + tan(b)
1-tan(a)tan(b)

 

[DrPhil]

Hi, I can't figure out this problem. I used a for alpha, and b for beta.
Verify the identity:

cos(a + b) 1-tan(a)tan(b)
cos(a - b) = 1+tan(a)tan(b)

As far as I got: cos(a)cos(b)-sin(a)sin(b)
cos(a)cos(b)+sin(a)sin(b)
Any help would greatly be appreciated, because I am new to all this Trig identity stuff.

BTW I know that the identity for tan(a + b)= tan(a) + tan(b)
1-tan(a)tan(b)

For the left side, you got as far as

\(\displaystyle \dfrac{\cos a \cos b - \sin a \sin b}{\cos a \cos b + \sin a \sin b} \)

So close! What if you divide all terms (both numerator and denominator) by \(\displaystyle \cos a \cos b \) ?

 

[monkey12]

Thank you, I see how to do it now. I had this written down in the notes, but it didn't make sense at first, lol.