# Simplify the expression #(sin(a)cos(b)+cos(a)sin(b))/(cos(a)cos(b)-sin(a)sin(b)) * (cos(a)cos(b)+sin(a)sin(b))/(sin(a)cos(b)-cos(a)sin(b))#?

##### 2 Answers

# tan(a+b) * cot(a-b) #

#### Explanation:

The expression is:

# E=(sin(a)cos(b)+cos(a)sin(b))/(cos(a)cos(b)-sin(a)sin(b)) * (cos(a)cos(b)+sin(a)sin(b))/(sin(a)cos(b)-cos(a)sin(b)) #

We can us the sine and cosine sum identities:

# sin(A+B)=sinAcosB+cosAsinB #

# sin(A-B)=sinAcosB-cosAsinB #

# cos(A+B)=cosAcosB-sinAsinB #

# cos(A-B)=cosAcosB+sinAsinB #

Applying these identities we can rewrite the expression as:

# E = (sin(a+b))/(cos(a+b)) * (cos(a-b))/(sin(a-b)) #

# \ \ \ = tan(a+b) * cot(a-b) #

#### Explanation:

To solve this, you need to know these formulae:

If you replace

Similarly, replacing

Now let's move on to the question.

Simplifying all the terms, we get