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

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Trigonometrical Equations

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

A

$110$

B

$191$

C

$80$

D

$194$

Solution

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

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

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

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

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

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

Standard 11

Mathematics

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