Question

simplify sec^-1(1/2x^2-1)​

Answer 1

Answer:

Hope it helps

here is your answer

2 cos-1x

Answer 2

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

$\blacksquare$QUESTION

SIMPLIFY

$\displaystyle \: {sec}^{ - 1} \: \frac{1}{ 2 {x}^{2} -1 }$

CALCULATION

Let

$x = cos \theta$

Then

$\displaystyle \: {sec}^{ - 1} \: \frac{1}{ 2 {x}^{2} - 1}$

$= \displaystyle \: {sec}^{ - 1} \: \frac{1}{ 2 {cos}^{2} \theta - 1 }$

$= \displaystyle \: {sec}^{ - 1} \: \frac{1}{ cos2\theta }$

$= \displaystyle \: {sec}^{ - 1} \: {(sec \: 2 \theta) }$

$= 2 \theta$

$= 2 \: { \cos}^{ - 1} x \: \: \: \: ( \because \: \theta \: = { \cos }^{ - 1} x)$