If cot⁡A + cos⁡A = m and cot⁡A - cos⁡A = n, then:

Correct option is B

​Given:

m = cot⁡A + cos⁡A

n = cot⁡A − cos⁡A 

Formula Used:

$$m^2 - n^2 = (m + n)(m - n)$$​

Solution:

Add m and n: 

m + n = cot⁡A + cos⁡A + (cot⁡A − cos⁡A) 

m + n = 2cot⁡A 

Subtract m and n: 

m - n = cot⁡A + cos⁡A - (cot⁡A − cos⁡A) 

m − n = 2cos⁡A

Square difference:

$$(m^2 - n^2)^2 \\ \ \\= (2 \cot A \cdot 2 \cos A)^2\\ \ \\ = 16 \cot A \cos A \\ \ \\= 16 \ mn$$​