Question

please solve it with steps

Answer 1

(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!