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16 vote

If θ is an acute angle and tan θ + cot θ = 2, then the value of tan5 θ + cot5 θ is

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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


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27 vote
Answered by on | Votes 27 |

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

= 2

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