If tan A + cot A = 5; find the value of tan2 A + cot2 A.

tan A + cot A = 5 Squaring both sides, (tan A \+ cot A)2 = 52 ⇒ tan2 A \+ cot2 A \+ 2 x tan A x cot A = 25 ⇒ tan2 A \+ cot2 A \+ 2 x tan A x = 25 ⇒ tan2 A \+ cot2 A \+ 2 x x = 25 ⇒ tan2 A \+ cot2 A \+ 2 = 25 ⇒ tan2 A \+ cot2 A = 25 \- 2 ⇒ tan2 A \+ cot2 A = 23 Hence, tan2 A + cot2 A = 23.