Question

If y = `cos^-1 ((x + 1)/(x - 1)) + "cosec"^-1 ((x - 1)/(x + 1))`, then `("d"y)/("d"x)` is ______.

विकल्प

• 1

• `(x - 1)/(x + 1)`

• `(x + 1)/(x - 1)`

• 0

Answer 1

If y = `cos^-1 ((x + 1)/(x - 1)) + "cosec"^-1 ((x - 1)/(x + 1))`, then `("d"y)/("d"x)` is 0.

Explanation:

y = `cos^-1 ((x + 1)/(x - 1)) + "cosec"^-1 ((x - 1)/(x + 1))`

= `cos^-1 ((x + 1)/(x - 1)) + sin^-1 ((x + 1)/(x- 1))`

∴ y = `pi/2`  ......`[because sin^-1x + cos^-1x = pi/2]`

∴ `("d"y)/("d"x)` = 0