If θ is an acute angle and tan θ + cot θ = 2, then the value of tan5 θ + cot5 θ is
1). 1
2). 2
3). 3
4). 4
Given that, tan θ + cot θ = 2
We know that cotθ = 1/tanθ
$(\Rightarrow tan{\rm{\theta }} + \frac{1}{{{\rm{tan\theta }}}} = 2)$
⇒tan2θ + 1 = 2tanθ
⇒tan2θ + 1 - 2tanθ = 0
⇒ (tanθ – 1)2 = 0
⇒tanθ = 1
cotθ = 1/tanθ
=1/1
=1
tan5 θ + cot5 θ = (1)5 +(1)5
= 26. If (x - y) = 7, then what is the value of $(x - 15)^{3} - (y - 8)^{3}$?