Question

what is the formula of tan (A-B)​

Answer 1

tan(A + B) = (sin A cos B + cos A sin B) / (cos A cos B − sin A sin B) (50) tan(A + B) = (tan A + tan B) / (1 − tan A tan B) Now if you replace B with −B, you have the formula for tan(A − B).

Answer 2

$\boxed{tan(A-B)=\dfrac{tanA-tanB}{1+tanA\:tanB}}$

Step-by-step explanation:

We know that,

$sin(A-B)=sinA\:cosB-cosA\:sinB$ ... (1)

$cos(A-B)=cosA\:cosB+sinA\:sinB$ ... (2)

Now, dividing (1) by (2), we get

${tan(A-B)}$

$=\dfrac{sinA\:cosB-cosA\:sinB}{cosA\:cosB+sinA\:sinB}$

$=\dfrac{1-tanA}{1+tanA\:tanB}$

• Dividing both the numerator and the denominator by $cosA\:cosB$

• since $tanA=\dfrac{sinA}{cosA}$

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