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Find the value of x for which function a...

Find the value of `x` for which function are identical. `f(x)=cosxa n dg(x)=1/(sqrt(1+tan^2x))`

Text Solution

Verified by Experts

`f(x)=cos x` has domain R and range `[-1,1]`
`g(x)=(1)/(sqrt(1+tan^(2)x))=(1)/(sqrt(sec^(2)x))=|cosx|,`
has domain `R-{(2n+1)pi//2, n in Z` as `tan x` is not defined for `x=(2n+1)pi//2, n in Z`
Also range of `g(x)=|cosx|` is `[0,1]`
Hence f(x) and g(x) are identical if x lies in first and fourth quadrant.
`implies x in underset(n in Z)(cup)(-(pi)/(2)+2n pi,(pi)/(2)+2n pi)`
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