Question

the value of tan(A+B).tan(A-B)

Answer 1

Answer:

Please check.

And mention in which form u want the answer

Answer 2

Concept

The formula will use to solve the problem

1. tan(A+B) = (tanA + tanB)/(1 - tanAtanB)

2. tan(A-B) = (tanA - tanB)/(1 + tanAtanB)

3. a² - b² = (a-b) (a+b)

Given

The expression tan(A+B).tan(A-B).

To find

We have to simplify the expression.

Solution

To simplify the given expression expand the formula.

tan(A+B).tan(A-B) $=\frac{\tan A+ \tan B}{1-\tan A \tan B } \times\frac{\tan A- \tan B}{1+\tan A \tan B}$

                             $=\frac{\tan^2 A- \tan^2 B}{1-\tan^2 A \tan^2 B}$

                            $=\frac{\sin^{2} A - \sin^2 B}{\cos ^{2}A \cos ^{2}B-\sin^{2} A\sin^{2} B}$

Hence the final answer is  $\frac{\sin^{2} A - \sin^2 B}{\cos ^{2}A \cos ^{2}B-\sin^{2} A\sin^{2} B}$.