Question

tan(a+b)/cot(a-b)=tan^2a-tan^2b/1-tan^2a tan^2b​

Answer 1

Answer:

proved

Step-by-step explanation:

Given  

tan(a+b)/cot(a-b)=tan^2a-tan^2b/1-tan^2a tan^2b

Given tan (A + B) / cot (A – B)

We know that 1/ cot = tan, so we have

tan (a + b) tan (a – b)

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

We know that a^2 – b^2 = (a + b)(a – b)

           = tan^2 A – tan^2 B / 1 – tan^2 A tan^2 B