if tan a+ cot a =4 then (tan)^4 a +(cot)^4 a =

Question

a)254 b) 256 c)196 d)194

Answer 1

tan^2 A + 1 = 4 * tan A

tan ^2 A - 4 tan A + 1 = 0

z ^2 - 4z + 1 = 0 <--- let z = tan A

z = [4 +or- sqrt ( 16 - 4) ]/ 2

= [ 4 +or- sqrt(12)]/2

= [ 4 +or- 2*sqrt(3)]/2

= 2 +or- sqrt(3)

THe positive branch, when passed to the arctangenet function, is 75 degrees

THe negative branch, likewise, is 15 degrees

so tan(75)^4 + 1/ tan(75)^4 = 194

while tan(15)^4 + 1/tan(15)^4 blows up