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Find the range of f(x)=1/(1-3sqrt(1-sin^...

Find the range of `f(x)=1/(1-3sqrt(1-sin^2x))`

Text Solution

Verified by Experts

The correct Answer is:
`(-oo,1//2] cup [1,oo)`
`f(x)=(1)/(1-3sqrt(1-sin^(2)x))=(1)/(1-3sqrt(cos^(2)x))`
`=(1)/(1-3|cosx|)`
Now, `-3|cosx| in [-3,0]`
or `1-3|cosx| in[-2,1]`
or `(1)/(1-3|cosx|) in (-oo,-1//2] cup [1,oo)`
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