Question

Tan A +Cot A=4 than tan^4A+ cot^4A =?

Answer 1

Given:

Tan A + Cot A = 4

Squaring on both sides,

(Tan² A + Cot² A) = (4)²

Tan² A + Cot² A + 2 (Tan A)(Cot A)  = 16

Tan² A + Cot² A + 2 = 16

(as Tan A × Cot A = 1)

Tan² A + Cot² A = 14

Again squaring on both sides,

(Tan² A + Cot² A)² = (14)²

Tan⁴ A + Cot⁴ A + 2 (Tan A)(Cot A) = 196

Tan⁴ A + Cot⁴ A + 2 = 196

(as Tan² A × Cot² A = 1)

Tan⁴ A + Cot⁴ A = 194


Hence Tan⁴ A + Cot⁴ A = 194


☺ ☺ ☺ Hope this Helps ☺ ☺ ☺