Consider the function defined by f(x) = sin x 1 + ^ 2 x + cos x 1 +...

(i), (ii) and (iv) are clearly false, since $f$\left(x\right)$is not defined for \dfrac{k\pi}{2} ,on the contrary the two RHS included in choices (i), (ii) and (iv) are defined for all x.<br /><br />(iii) is true since$f\left(x\right) = sin x\left|\cos x | + cos x\right|\sin x |$<br /><br />$f\left(x\right) = sin xcos x - cos xsin x = 0$for \dfrac{\pi}{2}$< x < \pi