Prove that `x+1/x=sintheta` is not possible for all `x in R`

Is costheta = x+1/x possible for x in R?

Prove that f (x) = |x-1|,x in R is not differnentiable at x=1

if f(xy) = f(x) f(y) for all x and y and if f(x) is continuous at x = 1, then show that it is continuous for all x except 0

Prove that f (x) = [X] is discontinuous for integral values of x.

Eliminate theta x=a sintheta , y=a costheta

Prove that f (x) =|x| is continuous at x =0

Prove that f : R rarr R, f(x)=4x-5 is invertible and find f^-1(x) .

Prove that sintheta/(1+costheta) + (1+costheta)/sintheta = 2cosectheta

Prove that log_a x+log_(1/a) x=0