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Find the range of f(x)=sqrt(4-sqrt(1+tan...

Find the range of `f(x)=sqrt(4-sqrt(1+tan^2x))`.

Text Solution

Verified by Experts

The correct Answer is:
`[0, sqrt3]`
`f(x)=sqrt(4-sqrt(1+tan^2x))`
`=sqrt(4-sqrt(sec^2x))`
`=sqrt(4-abs secx) `
`abs(secx)ge-1`
`or -abssecxle-1`
`or 4-abssecxle3`
`rArr sqrt(4-sqrt(1+tan^2x)) in[0,sqrt3]`
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