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3.Trigonometrical Ratios, Functions and Identities
easy
જો $\tan A + \cot A = 4,$ તો ${\tan ^4}A + {\cot ^4}A$ =
A
$110$
B
$191$
C
$80$
D
$194$
Solution
(d) $\tan A + \cot A = 4$
$ \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.$
Standard 11
Mathematics
