Prove that: (tan(A + B)) / (cot(A - B)) = (tan2A - tan2B) / (1 - tan2A × tan2B)

Question

Shiksha Nation · Accepted Answer

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

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

= (tan2A - tan2B) / (1 - tan2A tan2B)

Prove that: (tan(A + B)) / (cot(A - B)) = (tan²A - tan²B) / (1 - tan²A × tan²B)