AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper

The equation is given as,
y=sin2(cot−1√‌

1+x

1−x

)
Substitute x=cos‌2‌θ‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I)
y=sin2(cot−1√‌

1+cos‌2‌θ

1−cos‌2‌θ

)
y=sin2(cot−1√‌

2cos2θ

2sin2θ

)
y=sin2(cot−1(cot‌θ))
y=sin2θ‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II)
Differentiate the above equation with respect θ
‌

dy

dθ

=2‌sin‌θ‌cos‌θ
‌

dy

dθ

=sin‌2‌θ‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(III)
Differentiate the above equation (I) with respect θ
‌

dx

dθ

=−2‌sin‌2‌θ‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(IV)
From equation (III) and (IV) ‌

dy∕dθ

dx∕dθ

=‌

sin‌2‌θ

−2‌sin‌2‌θ

‌

dy

dx

=‌

−1

2