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

Let f:(-1,1)rarr R be such that f(cos4 theta)=(2)/(2-sec^(2)theta) for theta in(0,(pi)/(4))uu((pi)/(4),(pi)/(2)). Then the value(s) of f((1)/(3)) is/are

Let f:(-1,1)vec R be such that f(cos4 theta)=(2)/(2-sec^(2)theta) 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))(b)1+sqrt((3)/(2))(c)

If 8 cos 2 theta + 8 sec 2theta = 65, 0 lt theta lt (pi)/(2) then the value of 4 cos 4 theta is

Let f(theta)=(cot theta)/(1+cot theta) and alpha+beta=(5 pi)/(4) then the value f(alpha)f(beta) is

sin^(4)theta+cos^(4)theta=1-(1)/(2)f(theta) then f((pi)/(4)) =

If f(theta) = 1 + sin [pi/4 + theta] + cos (pi/4 + theta) . find the range of values of f(theta)

If f(theta) = 1 + sin [pi/4 + theta] + cos (pi/4 + theta) . find the range of values of f(theta)