( tan (3 π/8))2013+(- cot (3 π/8))2013 is

Question

( tan (3 π/8))2013+(- cot (3 π/8))2013 is (A) even integer (B) odd integer (C) rational which is not an integer (D) irrational

Tardigrade Admin · Accepted Answer

( tan (3 π/8))2013+(- cot (3 π/8))2013=(√2+1)2013-(√2-1)2013 =2[ 2013 C 1(√2)2012+ 2013 C 3(√2)2010+ 2013 C 5(√2)2008+ ldots ldots .+ 2013 C 2013(√2)0] = which is an even integer ⇒ (A)

Q. $(tan \frac{3 π}{8})^{2013} + (- cot \frac{3 π}{8})^{2013}$ is

even integer

odd integer

rational which is not an integer

irrational

$(tan \frac{3 π}{8})^{2013} + (- cot \frac{3 π}{8})^{2013} = (2 + 1)^{2013} - (2 - 1)^{2013}$
$= 2 [^{2013} C_{1} (2)^{2012} +^{2013} C_{3} (2)^{2010} +^{2013} C_{5} (2)^{2008} + \dots\dots . +^{2013} C_{2013} (2)^{0}]$
$=$ which is an even integer $\Rightarrow$ (A)

Q. (tan83π​)2013+(−cot83π​)2013 is