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Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(...

Let `f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x`. Then the sum of the maximum and minimum values of f(x) is

A

`pi`

B

`2pi`

C

`3pi`

D

`pi/2`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=sin^(-1)2x+cos^(-1)2x+sec^(-1)2x`
`f(x)=pi/2+sec^(-1)2x`
`f(x)=pi/2+sec^(-1)2x`
Graph of `sec^(-1)2x` is as following
`(f(x))_("minimum")=pi/2+0=pi/2`
`(f(x))_("minimum")=pi/2+pi=(3pi)/2`
Sum `=pi/2+(3pi)/2`
`2pi`
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