Let `f:(-1,1)vecR` be such that `f(cos4theta)=2/(2-sec^2theta)` for `theta in ` `(0,pi/4)uu(pi/4,pi/2)` . Then the value(s) of `f(1/3)` is (are) (a)`1-sqrt(3/2)` (b) `1+sqrt(3/2)` (c) `1-sqrt(2/3)` (d) `1+sqrt(2/3)`

Explanation

It is given that,

`f(cos4theta) = 2/(2-sec^2theta)`

We have to find `f(1/3)`.

So, we can consider,

`cos4theta = 1/3`

Now,

`cos4theta = 2cos^2 2theta -1`

`=>cos2theta = +-sqrt((1+cos4theta)/2 )`

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