IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

Harsh137

cos y = x cos (a + y) => x = cos y/ cos(a+y)
Differentiating w.r.t. x

-sin y dy/dx = x*(-sin(a+y)*dy/dx) + cos(a+y)*dx/dx
-sin y y'= -x sin(a+y) y' + cos(a+y) ........[dy/dx=y']
y'(x sin(a+y) - sin y)=cos(a+y)
y'= cos (a+y)/(x sin(a+y) - sin y)
=cos(a+y)/[{cos y sin(a+y)/cos(a+y)} - sin y]
=cos²(a+y)/[cos y sin(a+y) - sin y cos(a+y)]
=cos²(a+y)/sin(a+y-y)

dy/dx= [cos²(a+y)] / [sina]

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