If tanA + cotA = 4,then the value of tan4A + cot4A will be equal to?

Question

here, 4 is the power of tan and cot, for example, 8 = 2 having power 3.

Answer 1

tan A + cot A = 4
square both sides

tan^2 A + cot^2 A +2 = 16 (using (a+b)^2 and tan A is inverse of cot A)
or tan^2 A + cot^2 A = 14

square again an
tan^4 A + cot^4 A +2 = 196
so tan^4 A + cot^4 A = 194

Answer 2

Cota 4

Answer 3

tanA + cotA =4 =
tanA + 1/tanA
tan^2A - 4tanA + 1 = 0
TanA = (4+/-sqrt(16-4))/2
= 2+/-sqrt(3)
tan^4A+cot^4A =194

Answer 4

tanA + cotA=4
tanA + 1/tanA=4 (since cotA=1/tanA)
tan2A + 1 = 4tanA (2 is the power of tan)
tan2A - 4tanA +1=0
solve this equation and then proceed

Answer 5

tanA^4 +cotA^4= (tanA^2 +cotA^2 )^2- 2tanA^2cotA^2
={ (tanA + cot)^2 - 2tanAcotA}^2 - 2
= { (4)^2 -2} -2
= 12

Answer 6

There are 2 answers.

let x=tan(a)
x+1/x=4
x^2+1=4x
x^2-4x+1=0
x1=2+sqrt(12)/2=2+sqrt(3)
x2=2-sqrt(3)

arctan(x1)=75 degrees
arctan(x2)=15 degrees

tan(4*75)=tan(300)=-sqrt(3) so
tan(300)+cot(300)=-sqrt(3)-1/sqrt(2)=(4/3)sqrt(3)=-2.3094
tan(4*15)=tan(60)=sqrt(3)
&
tan(60)+cot(60)=sqrt(3)+1/sqrt(3)=(4/3)sqrt(3)=2.3094