Question

x=a(cos2t+2tsin2t) and y=a(sin2t-2tcos2t)

then find d^2 y/dx^2​

Answer 1

Answer:

Step-by-step explanation:

x=a(cos2t+2tsin2t)

dt

dx

​  

=a(−2sin2t+2sin2t+4tcos2t)=4at cos2t

dt  

2

 

d  

2

x

​  

=4acos2t−8atSin2t

y=a(sin2t−2tcos2t)

dt

dy

​  

=a(2cos2t−2cos2t+4tsin2t)=4atsin2t

dt  

2

 

d  

2

y

​  

=4aSin2t+8atcos2t

So  

dx  

2

 

d  

2

y

​  

=  

4Cos2t−8tSin2t

4Sin2t+8tCos2t

​