A) \[\frac{2}{1-2\,{{\cos }^{2}}\theta }\]
B) \[\frac{2}{2\,{{\sin }^{2}}\theta -1}\]
C) both (a) & (b)
D) None of these
Correct Answer: C
Solution :
(c): \[\frac{{{(sin\theta +cos\theta )}^{2}}+{{(sin\theta -cos\theta )}^{2}}}{{{\sin }^{2}}\theta -{{\cos }^{2}}\theta }\] \[=\frac{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta +2\sin \theta \cos \theta +{{\sin }^{2}}\theta +{{\cos }^{2}}\theta -2\sin \theta \cos \theta }{{{\sin }^{2}}\theta -{{\cos }^{2}}\theta }\] \[=\frac{2}{{{\sin }^{2}}\theta -{{\cos }^{2}}\theta }=\frac{2}{1-2{{\cos }^{2}}\theta }=\frac{2}{2{{\sin }^{2}}\theta -1}\]
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