A) 110
B) 191
C) 80
D) 194
Correct Answer: D
Solution :
\[\tan A+\cot A=4\] \[\Rightarrow \,{{\tan }^{2}}A+{{\cot }^{2}}A+2\,\tan A\,\,\cot A=16\] \[\Rightarrow \,{{\tan }^{2}}A+{{\cot }^{2}}A=14\,\,\Rightarrow \,{{\tan }^{4}}A+{{\cot }^{4}}A+2=196\] \[\Rightarrow \,{{\tan }^{4}}A+{{\cot }^{4}}A=194.\]
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