Thank you for reporting, we will resolve it shortly
Q.
If $\left|s i n^{2} x + 10 - x^{2}\right|=\left|9 - x^{2}\right|+2sin^{2}x+cos^{2}x,$ then $x$ lies in
NTA AbhyasNTA Abhyas 2020
Solution:
$\left|s i n^{2} x + 10 - x^{2}\right|=\left|9 - x^{2}\right|+sin^{2}x+\left(s i n^{2} x + c o s^{2} x\right)$
$\Rightarrow \left|s i n^{2} x + 1 + 9 - x^{2}\right|=\left|9 - x^{2}\right|+sin^{2}x+1$
$\left|x + y + z\right|=\left|x\right|+\left|y\right|+\left|z\right|$ , if $x,y,z$ have the same sign
$\Rightarrow sin^{2}x\left(9 - x^{2}\right)\geq 0$
$\Rightarrow \left(9 - x^{2}\right)\geq 0$
$\Rightarrow x\in \left[- 3,3\right]$