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If y = sec^(-1) [ "cosec x"] + "cosec"^...

If `y = sec^(-1) [ "cosec x"] + "cosec"^(-1) [sec x] + sin^(-1) [cos x] + cos^(-1)[sinx ], "then "(dy)/(dx) ` is equal to

A

0

B

2

C

`-2`

D

`-4`

Text Solution

Verified by Experts

The correct Answer is:
D
Given , `y= sec^(-1) ("cosec x") + "cosec"^(-1) (sec x) + sin^(-1) (cos x) + cos^(-1) (sin x)`
`= sec^(2) [ sec((pi)/(2) - x)] + "cosec"^(-1) [ "cosec" ((pi)/(2)) - x)]+ sin^(-1) [ sin"" ((pi)/(2)- x)]+ cos^(-1) [ cos ((pi)/(2)- x)]`
`= (pi)/(2) - x + (pi)/(2) - x + (pi)/(2) - x + (pi)/(2) - rArr y = 2pi - 4x `
On differentiating both sidews w.r.t.x, we get
` rArr (dy)/(dx) = - 4 ` .
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