A) \[\frac{\sqrt{5}-1}{4}\]
B) \[\frac{\sqrt{5}+1}{8}\]
C) \[\frac{\sqrt{3}-1}{4}\]
D) \[\frac{\sqrt{3}+1}{2\sqrt{2}}\]
Correct Answer: B
Solution :
\[{{\cos }^{2}}A-{{\sin }^{2}}B=\cos \,(A+B)\,.\,\cos \,(A-B)\] \[\therefore \,\,{{\cos }^{2}}{{48}^{o}}-{{\sin }^{2}}{{12}^{o}}=\cos \,\,{{60}^{o}}\,.\,\cos \,\,{{36}^{o}}\] \[=\frac{1}{2}\,\left( \frac{\sqrt{5}+1}{4} \right)=\frac{\sqrt{5}+1}{8}.\]
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