Question

simplify sec ^-1 (1/ 1-2x^2​)

Answer 1

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$\blacksquare$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 2

Answer:

hey.

Step-by-step explanation:

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