If A + A = 4, then ^4 A + ^4 A is equal to - Vidyadip

MCQ

If $\tan A + \cot A = 4,$ then ${\tan ^4}A + {\cot ^4}A$ is equal to

A
$110$
B
$191$
C
$80$
✓
$194$

✓

Answer

Correct option: D.

$194$

d
(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.$

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