Question

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

• A. $110$
• B. $191$
• C. $80$
• D. $194$

Answer 1

Answer: (D)

$194$

Answer 2

$tan\,A+cot\,A=4\quad\ldots\left(i\right)$ Squaring $\left(i\right)$ both sides, we get $tan^{2}A+cot^{2}A=14\quad\ldots\left(ii\right)$ Squaring $\left(ii\right)$ both sides, we get $tan^{4}A+cot^{4}A=194$.