If tan A + cot A = 4,


If tan A + cot A = 4, then write the value of tan4 A + cot4 A.


$\tan A+\cot A=4$

Squaring both the sides :

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

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

Squaring both the sides again:

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

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

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