Question

if m cotA = n find value m sinA - n cosA/ n cosA + m sinA

Answer 1

see i will guide u

take cot A =n/m and then

expand  all the terms in for of p/b h/b etc. etc. and put the values u will get the answer

hope u fr happy nd my explanation helped you

Answer 2

Answer:

$\dfrac{m\sin A-n\cos A}{m\sin A+n\cos A}=\dfrac{m^2-n^2}{m^2+n^2}$

Step-by-step explanation:

Given: m cot A = n

To Determine: $\dfrac{m\sin A-n\cos A}{n\cos A+m\sin A}$

Calculation:

$m\cot A=n$

$\dfrac{\cos A}{\sin A}=\dfrac{n}{m}$

Now multiply both side by n/m

$\dfrac{n\cos A}{m\sin A}=\dfrac{n^2}{m^2}$

Using Componendo and Dividendo

$\dfrac{n\cos A-m\sin A}{n\cos A+m\sin A}=\dfrac{n^2-m^2}{n^2+m^2}$

Taking minus sign from numerator and flip the term

$\dfrac{m\sin A-n\cos A}{m\sin A+n\cos A}=\dfrac{m^2-n^2}{m^2+n^2}$