If tanA + cotA = 4, then tan^4A + cot^4A is equal to - Vidyadip

MCQ

If $tanA + cotA = 4$, then $tan^4A + cot^4A$ is equal to

A
$110$
B
$191$
C
$80$
✓
$194$

✓

Answer

Correct option: D.

$194$

d
$(\tan A+\cot A)^{2}=16$

$\Rightarrow \quad \tan ^{2} A+\cot ^{2} A+2=16$

$\Rightarrow \quad \tan ^{2} A+\cot ^{2} A=14$

$\Rightarrow \quad\left(\tan ^{2} A+\cot ^{2} A\right)^{2}=196$

$\Rightarrow \quad \tan ^{4} A+\cot ^{4} A+2=196$

$\Rightarrow \quad \tan ^{4} A+\cot ^{4} A=194$

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