the value of tan (60deg.) - cot( 60 deg.) is? whether +/- rational or irrational?

Question

plz show me working

thank you

Answer 1

tan(60deg.)=root 3
cot(60deg.)=1/root3
subtracting these two we get
root3- __1___ =[(root 3)*(root3)-1]/(root3)
root 3

Therefore it is equal to [3-1]/(root3)=2/(root3)

So by this we can say that it is positive irrational number as root 3 is irrational.

Answer 2

value of tan 60d =√3
cot is reverse of tan
than value of cot =1/√3
according to equation
tan60 d -cot60 d
put value
√3 - 1/√3
solve
2/√3 answers
answer is +ve than irrational.

Answer 3

tan 60° = 3^1/2
cot 60° = (3^1/2)3

so tan 60° -cot 60° = 3^1/2 -(3^1/2)/3 = 2*(3^1/2) /3

Answer 4

tan 60 = root 3
cot 60 = 1/ root 3
r3 - 1/ r3
=3 - 1/ r3
= 2 / r3
the ans is +ve nd irrational

Answer 5

always remember that if the ur angle is lie in first quadrant than it will always + value. There fore cot(60) is + value and
-cot60 have negative value which is irrational number

Answer 6

tan(60)-cot(60)
= (3^1/2) -(1/(3^1/2))
= ((3^1/2)*(3^1/2) - 1) /(3^1/2) {taking L.C.M}
= (3-1)/(3^1/2)
= 2/(3^1/2)
= (2 * (3^1/2))/3
therefore, it is positive and irrational

Answer 7

tan(60deg) = sqrt(3)
cot(60deg) = 1/sqrt(3)
tan(60deg) - cot(60deg) = sqrt(3) - 1/sqrt(3) = 2/3 * sqrt(3)

The answer is + irrational.

Answer 8

Maybe to a rational person. But not to an irrational person.

Answer 9

tan 60 degree is root of 3....cot is its inverse so its 1/root of 3