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Previous Year Question (PYQs)
1
Differentiate y = sin⁻¹((1 - x²)/(1 + x²)), 0 < x < 1 with respect to x.
Solution
Put $x=\tan \theta$
$ \Rightarrow \frac{1-x^2}{1+x^2}=\frac{1-\tan^2\theta}{1+\tan^2\theta}=\cos 2\theta $
So,
$ y=\sin^{-1}(\cos 2\theta) $
Now important step (range use):
Since $0
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