UPSC NDA I 2025 Mathematics Paper

Given,
The function is y=sin‌−1(x−‌

4x3

27

), and we are tasked with simplifying it.
y=sin‌−1(x−‌

4x3

27

)
We recognize that we can factor the expression as:
x−‌

4x3

27

=(‌

x

3

)(3−4(‌

x

3

)3)
Thus, the function becomes:
y=sin‌−1(‌

x

3

(3−4(‌

x

3

)3))
Recognizing that this fits a known identity for inverse trigonometric functions:
sin‌−1(x)=3sin‌−1(‌

x

3

)
Thus, we can simplify the expression to:
y=3sin‌−1(‌

x

3

)