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Write True or False and justify your answer in each of the following:
W
(i) The value of \( \sin \theta \) is \( x+\frac{1}{x} \), where \( x \) is a positive real number.
(ii) \( \cos \theta=\frac{a^{2}+b^{2}}{2 a b} \), where \( a \) and \( b \) are two distinct numbers such that \( a b0 \).
(iii) The value of \( \cos ^{2} 23-\sin ^{2} 67 \) is positive.
(iv) The value of the expression \( \sin 80^{\circ}-\cos 80^{\circ} \) is negative.
(v) The value of \( \sin \theta+\cos \theta \) is always greater than 1 .
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