Question

Differentiate with respect to x :

If y = sec-1 ( x + 1 / x - 1 ) + sin-1 ( x -1 / x + 1 ), show that dy/dx = 0

Answer 1

$y = { \sec }^{ - 1} ( \frac{x + 1}{x - 1} ) \: + { \csc }^{ - 1} ( \frac{x + 1}{x - 1} )$
we know that
${ \sec }^{ - 1} x + { \csc }^{ - 1} x = \frac{\pi}{2}$
$y = \frac{\pi}{2}$
$\frac{dy}{dx} = 0$


Mark this answer as brainliest answer

Answer 2

Answer:

Step-by-step explanation:

Sec. ^-1= 1/cos^-1

Hence... Cos^-1(x-1/x+1) + sin ^-1 ( x-1/x+1)

We know sin^-1 +cos^-1=pi/2

Hence answer = pi /2

Differentiating pi/2 gives...0

So...0 is the anwer