Let f : (-1, 1) -> R be such that f(cos4...

Let `f : (-1, 1) -> R` 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 pm sqrt((3)/(2))`

B

`1pm sqrt((2)/(3))`

C

`1pm sqrt((1)/(3))`

D

`1pm sqrt((1)/(2))`

Verified by Experts

The correct Answer is:

A

Similar Questions

Explore conceptually related problems

Let f:(-1,1) rarrR be such that f(cos4theta)=2/(2-sec^2theta) for thetain(0,pi/4)cup(pi/4,pi/2) . The the values of f(1/3) are

Prove that sin^4 theta - cos^4 theta = 1 - 2cos^2 theta

If 8 cos 2theta+8sec2theta=65 , 0<(theta)<(pi/2) then the value of 4 cos 4theta is equal to

If sin^2 theta=1/4 , then value of theta is

Values of theta satisfying the eqation sintheta+sin7theta=sin4theta for theta in (0, pi/2) are

If xcostheta=ycos(theta+(2pi)/3)=zcos(theta+(4pi)/3) then the value of 1/x+1/y+1/z is equal to

If x\ costheta=y cos(theta+(2pi)/3)=z cos(theta+(4pi)/3) , then write the value of 1/x+1/y+1/zdot

If costheta=12/13 , 0 < theta < pi /2 , find the value of frac(1)(tan^2theta)

sin(pi+theta)sin(pi-theta)cosec^2theta=