Let \theta \in (0,\frac{\pi}{4}) and t_1=(\tan \theta)^{\tan \theta}, t_2=(\tan \theta)^{\cot

Anika Osborne

Anika Osborne

Answered question

2022-01-23

Let θ(0,π4) and t1=(tanθ)tanθ,t2=(tanθ)cotθ,t3=(cotθ)tanθ and t4=(cotθ)cotθ, then show that t4>t3>t1>t2.

Answer & Explanation

Appohhl

Appohhl

Beginner2022-01-24Added 11 answers

Hint:
In 0<θ<π4,
cotθtanθ=2cot2θ>0
cotθ>tanθ which is >0
Now if a>b>0, aaab=ab(aab1)>0
and similarly (ab)a>1aa>ba and so on
Karly Logan

Karly Logan

Beginner2022-01-25Added 11 answers

for θ(0,45)
tanθ(0,1)
lets take tanθ=12
t1=(tanθ)tanθ=120.7
t2=(tanθ)cotθ=122=0.25
t3=(cotθ)tanθ=2
t4=(cotθ)cotθ=22=4
t4>t3>t1>t2

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