# Thread: Trigonmetric Identity - Tan Theta

1. ## Trigonmetric Identity - Tan Theta

What you have to multiply for addition/subtraction identity, I was thinking of getting cosB or sinB out.

tan theta = cos (A+B) / sin (A+B)
= cosAcosB - sinAsinB / sinAcosB + cosAsinB

2. Originally Posted by Quan
What you have to multiply for addition/subtraction identity, I was thinking of getting cosB or sinB out.

tan theta = cos (A+B) / sin (A+B)
= cosAcosB - sinAsinB / sinAcosB + cosAsinB
First of all, use parenthesis.
$\displaystyle tan(\theta) = \frac{cos(A + B)}{sin(A + B)} = \frac{cos(A)cos(B) - sin(A)sin(B)}{sin(A)cos(B) + cos(A)sin(B)}$

not
$\displaystyle tan(\theta) = \frac{cos(A + B)}{sin(A + B)} = cos(A)cos(B) - \frac{sin(A)sin(B)}{sin(A)cos(B)} + cos(A)sin(B)$

-Dan

3. Originally Posted by topsquark
First of all, use parenthesis.
$\displaystyle tan(\theta) = \frac{cos(A + B)}{sin(A + B)} = \frac{cos(A)cos(B) - sin(A)sin(B)}{sin(A)cos(B) + cos(A)sin(B)}$

not
$\displaystyle tan(\theta) = \frac{cos(A + B)}{sin(A + B)} = cos(A)cos(B) - \frac{sin(A)sin(B)}{sin(A)cos(B)} + cos(A)sin(B)$

-Dan
Sorry, I'm looking for the addition / subtraction Identities for Tan Theta

4. Originally Posted by Quan
Sorry, I'm looking for the addition / subtraction Identities for Tan Theta
By the way, I missed this in the previous post:
$\displaystyle tan(\theta) = \frac{sin(\theta)}{cos(\theta)}$
not the other way around.

$\displaystyle tan(A + B) = \frac{sin(A + B)}{cos(A + B)} = \frac{sin(A)cos(B) + cos(A)sin(B)}{cos(A)cos(B) - sin(A)sin(B)}$

Now divide the numerator and denominator by $\displaystyle cos(A)cos(B)$:
$\displaystyle tan(A + B) = \frac{tan(A) + tan(B)}{1 - tan(A)tan(B)}$

-Dan