Trigonometric Identities Question 166
Question: If $ \tan A+\cot A=4, $ then $ {{\tan }^{4}}A+{{\cot }^{4}}A $ is equal to
[Kerala (Engg.) 2002]
Options:
A) 110
B) 191
C) 80
D) 194
Show Answer
Answer:
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. $
BETA
