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Find the value of $\sin 67\large\frac{1}{2}^{\large\circ}$ & $\cos 67\large\frac{1}{2}^{\large\circ}$

$\begin{array}{1 1}(a)\;\large\frac{1}{4}\normalsize[\sqrt{4+2\sqrt 2}+\sqrt{4-2\sqrt 2}],\large\frac{1}{4}\normalsize[\sqrt{4+2\sqrt 2}-\sqrt{4-2\sqrt 2}]\\(b)\;\large\frac{1}{2}\normalsize[\sqrt{4+2\sqrt 2}+\sqrt{4-2\sqrt 2}],\large\frac{1}{2}\normalsize[\sqrt{4+2\sqrt 2}-\sqrt{4-2\sqrt 2}]\\(c)\;\large\frac{1}{3}\normalsize[\sqrt{4+2\sqrt 2}+\sqrt{4-2\sqrt 2}],\large\frac{1}{4}\normalsize[\sqrt{4+2\sqrt 2}-\sqrt{4-2\sqrt 2}]\\(d)\;\large\frac{1}{4}\normalsize[\sqrt{4+2\sqrt 2}-\sqrt{4-2\sqrt 2}],\large\frac{1}{4}\normalsize[\sqrt{4+2\sqrt 2}+\sqrt{4-2\sqrt 2}]\end{array}$

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