Question

if m cot A=n then the value of m sinA-n cosA/n cos A+ m sinA is​

Answer 1

Answer:

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Answer 2

Answer:

(m sinA - n cosA)/(n cosA + m sinA)

 

Dividing the numerator (top) and denominator (bottom) by sinA

 

= [(m sinA - n cosA)/sinA]/[(n cosA + m sinA)/sinA]

= (m sinA/sinA  - n cosA/sinA)/(n cosA/sinA + m sinA/sinA)

= (m - ncotA)/(n cotA + m)

 

Since m cotA =n  or cotA = n/m, substituting it in the above expression, we get

 

= (m - n* n/m)/(n*n/m + m)

 

= [m - n^2/m]/[n^2/m + m]

 

= [(m^2 - n^2)/m]/[(n^2 + m^2)/m]

 

= [(m^2 - n^2)/m]  *[m/(n^2 + m^2)]

 

= (m^2 - n^2)/(n^2 + m^2)

 

Therefore, 

 

(m sinA - n cosA)/(n cosA + m sinA) =  (m^2 - n^2)/(m^2 + n^2)

 

I hope it helps!