Question:
If tan A + cot A = 4, then write the value of tan4 A + cot4 A.
Solution:
$\tan A+\cot A=4$
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:
$\tan ^{4} A+\cot ^{4} A+2=196$
$\Rightarrow \tan ^{4} A+\cot ^{4} A=194$