Let `f(x)=((2sinx+sin2x)/(2cosx+sin2x)*(1-cosx)/(1-sinx)): x in R.`
Consider the following statements.
I. Domain of f is R.
II. Range of f is R.
III. Domain of f is `R-(4n-1)pi/2, n in I.`
IV. Domain of f is `R-(4n+1)pi/2, n in I.`
Which of the following is correct?

If f(tanx)=sin2x: x ne (2n+1)(pi)/(2), n in I then which of the following is an incorrect statement?

If f(tanx)=sin2x: x ne (2n+1)(pi)/(2), n in I then which of the following is an incorrect statement?

Let f(x)=(sqrt2-(cosx+sinx))/(1-sin2x), x ne pi//4 . The value f(pi//4) so that f is continuous is (sqrt2=1.41)

The domain of f(x) =(1)/(1 -2cosx) is:

Let f(x) = sqrt(2-x-x^(2)) and g(x) = cos x . Which of the following statement are true ? (I) Domain of f((f(x))^(2)) = Domain of f(g(x)) (II) Domain of f(g(x)) + g(f(x)) = Domain of f(g(x)) (III) Domain of f(g(x)) = Domain of f(g(x)) (IV) Domain of g((f(x))^(3)) = Domain of f(g(x))

Consider the real-valued function satisfying 2f(sinx)+f(cosx)=xdot then the domain of f(x)i sR domain of f(x)i s[-1,1] range of f(x) is [-(2pi)/3,pi/3] range of f(x)i sR