Question

prove the following identities:
(a) tan(A-B)=(1-cot A tan B)/(cot A+tan B)

(b) cot(A-B)=(cot A cat B+1)/(cot B-cot A)

Answer 1

You know formula of tan(A-B)

Answer 2

tan(A-B)=(tan A-tan B)/(1+tan A tan B)

Answer 3

divide each term by tan A

Answer 4

to prove the identity

Answer 5

just a matter of rearranging the fraction
cotA = 1/tanA
\[\large \frac{1-\frac{\tan B}{\tan A}}{\frac{1}{\tan A}+\tan B} = \frac{\frac{\tan A-\tan B}{\tan A}}{\frac{1+\tan A \tan B}{\tan A}} = \frac{\tan A -\tan B}{1+\tan A \tan B}=\tan(A-B)\]