A) 1
B) 2
C) 0
D) 4
Correct Answer: B
Solution :
\[{{\sin }^{2}}7{{\frac{1}{2}}^{o}}+{{\sin }^{2}}82{{\frac{1}{2}}^{o}}\]\[+{{\tan }^{2}}{{2}^{o}}.{{\tan }^{2}}{{88}^{o}}\] \[={{\sin }^{2}}{{\frac{1}{2}}^{o}}+{{\sin }^{2}}\left( {{90}^{o}}-7{{\frac{1}{2}}^{o}} \right)+\]\[{{\tan }^{2}}{{2}^{o}}.ta{{n}^{2}}({{90}^{o}}-{{2}^{o}})\] \[={{\sin }^{2}}7{{\frac{1}{2}}^{o}}+{{\cos }^{2}}7{{\frac{1}{2}}^{o}}+{{\tan }^{2}}{{2}^{o}}.{{\cot }^{2}}^{o}\] \[[\because \,\,\sin ({{90}^{o}}-\theta )=\cos \theta ;\,\,\tan ({{90}^{o}}-\theta )=\cot \theta ]\] \[=1+1=2\]
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