Question

If siny=xsin(a+y), then dy/dx=

Answer 1

siny=xsin(a+y).

∴x=siny/sin(a+y).

Differentiating w.r.t. y, using the Quotient Rule, we have,

dx/dy=[sin(a+y)⋅ddy{siny}−siny⋅ddx{sin(a+y)}]/sin²(a+y),

=[sin(a+y)cosy−sinycos(a+y)⋅ddy(a+y)]/sin ²(a+y),...[The Chain Rule],

=sin(a+y)cosy−sinycos(a+y)/sin ²(a+y),

=sin{(a+y)−y}/sin ²(a+y),

=sina/sin²(a+y).

⇒dy/dx=1/(dx/dy=sin²(a+y)/sina.