different forms of complex sine function

Pick out the true statements:
(a) $|\sin z|≤1 ∀z∈\mathbb{C}$.
(b) $\sin^2z+\cos^2z=1 ∀z∈\mathbb{C}$.
(c) $\sin z =(e^{iz}-e^{-iz})/2 ∀z∈\mathbb{C}$.

(a) is not true for large z.
(b) true.
(c) true
Am I correct?

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(a) is not true but I don't know what you mean "large" $z$? I suppose you mean large in modulus? You can always use Liouville's Theorem of course for a more general result (or even the little Picard theorem for stronger results).
(c) is not true as you need a $i$ in the denominator.