Sec^-1( 1/ 1 - 2x^2)pls answer this fast

1.	Sec^-1( 1/ 1 - 2x^2)pls answer this fast
Answer» $\displaystyle\huge\red{\underline{\underline{Solution}}}$ $\blacksquare$ QUESTION SIMPLIFY $\displaystyle \: {sec}^{ - 1} \: \frac{1}{ 1- 2 {x}^{2} }$ CALCULATION Let $x = sin \theta$ Then $\displaystyle \: {sec}^{ - 1} \: \frac{1}{ 1- 2 {x}^{2} }$ $= \displaystyle \: {sec}^{ - 1} \: \frac{1}{ 1- 2 {sin}^{2} \theta }$ $= \displaystyle \: {sec}^{ - 1} \: \frac{1}{ cos2\theta }$ $= \displaystyle \: {sec}^{ - 1} \: {(sec \: 2 \theta) }$ $= 2 \theta$ $= 2 \: { \sin}^{ - 1} x \: \: \: \: ( \because \: \theta \: = { \sin }^{ - 1} x)$

Answer»

$\displaystyle\huge\red{\underline{\underline{Solution}}}$