If x sin ( A + y) + sinA cos (A + y) = 0, prove that dy/dx = [ - Maths - Continuity and Differentiability

Question

If x sin ( A + y) + sinA cos (A + y) = 0, prove that dy/dx = [
sin2(a + y)] / [ sin (a + y) - ycos ( a + y ) ]

Anuradha Sharma · Accepted Answer

Your question is wrong it should be,
xsin(a+y)=sin y , Now
 We have,x= sin y sin a+y⇒dxdy = sina + y 
 cos y - sin y cos a+ysina + y2       quotient rule                                                ⇒dxdy =cos y [sin a cos y + cos a sin y] - sin y[cos a cos y - sin a sin y]sin2a + y⇒dxdy =sin a cos2y + cos a sin y cos y - cos a sin y cos y + sin a sin2ysin2a + y⇒dxdy  = sin a cos2y  + sin a sin2y sin2a + y⇒dxdy  = sin a cos2y + sin2ysin2a + y⇒dxdy  =sin asin2a + y⇒dydx = sin2a + ysin a

If x sin ( A + y) + sinA cos (A + y) = 0, prove that dy/dx = [ sin2(a + y)] / [ sin (a + y) - ycos ( a + y ) ]

If x sin ( A + y) + sinA cos (A + y) = 0, prove that dy/dx = [ sin²(a + y)] / [ sin (a + y) - ycos ( a + y ) ]