If tan A + cot A = 4, then tan^4 A + cot^4 A

If tan A + cot A = 4, then tan4 A  + cot4 A is equal to

  1. 194
  2. 191
  3. 110
  4. 80

Answer

We have tan A + cot A = 4

Squaring both sides,

tan2 A + cot2 A + 2 = 16 (since cot A = 1 / tan A)

So, tan2 A + cot2 A = 14

Again squaring both sides, we have

tan4 A + cot4 A + 2 = 196

So, tan4 A + cot4 A = 194

The correct option is A.