If \theta is an acute angle and \tan\theta+\cot\theta=2. Find the va

glamrockqueen7

glamrockqueen7

Answered question

2021-08-15

If θ is an acute angle and tanθ+cotθ=2. Find the value of tan7θ+cot7θ

Answer & Explanation

coffentw

coffentw

Skilled2021-08-16Added 103 answers

Given:
tanθ+cotθ=2 and Q is acute angle
tan7θ+cot7θ
tanθ+cotθ=2
tanθ+1tanθ=2
tan2θ+1tanθ=2tan2θ+1=2tanθ
tan2θ2tanθ+1=0
tanθ(tanθ1)1(tanθ1)=0
(tanθ1)1(tanθ1)=0
tanθ1=0tanθ=1
tanθ=1
θ=95
So,
cotθ=1tanθ=11=1
Now, tan7θ+cot7θ
=(tanθ)7+(cotθ)7
=17+17
=1+1
tan7+cot7=2

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-10Added 2605 answers

Answer is given below (on video)

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