Question

tan + cot = 2 find the value of tan ^5 +cot^5

Answer 1

tanA + cotA = 2tan A + 1/tan A = 2[tan ^2 A + 1 ] / tan A = 2tan ^2 A -2 tan A + 1 =0(tan A -1)^2 =0tan A - 1 =0tan A = 1cot A = 1tan^5 A + cot^5 A= 1 + 1 = 2. I hope this answer is helpful to you

Answer 2

Tan A + cot A = 2 is only possible when angle A is 45degree.
Tan 45degree =1.
Cot 45 degree=1.
Therefore angle tan^5 + cot^5 = 1^5 + 1^5.
= 1 + 1= 2.
Hope it helps.