Question

Solve:

$\underset{x\to 0}{lim}\left[ln\left(1+{\sin }^{2}x\right).\tan \left(l{n}^2\left(1+x\right)\right)\right]$

Answer 1

given that, $\underset{x\to 0}{lim}\left[ln\left(1+{\sin }^{2}x\right).\tan \left(l{n}^2\left(1+x\right)\right)\right]$

$=\left[ln\right(1+si{n}^{2}0).tan(l{n}^2(1+0)\left)\right]$

$=\left[ln1.tan\right(l{n}^{2}1\left)\right]=0$