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Question

If θ(0,π4) and t1=(tanθ)tanθ, t2=(tanθ)cotθ, t3=(cotθ)tanθ and t4=(cotθ)cotθ then

A
t1>t2>t3>t4
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B
t4>t3>t1>t2
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C
t3>t1>t2>t4
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D
t2>t3>t1>t2
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Solution

The correct option is B t4>t3>t1>t2
θ(0,π4)tanθ<1 and cotθ>1.
Let tanθ=1x and cotθ=1+y. where x,y>0 and are very small, then
t1=(1x)1x,t2=(1x)1+y,t3=(1+y)1x,t4=(1+y)1+y
Clearly, t4>t3 and t1>t2. Also t3>t1.
Thus, t4>t3>t1>t2.

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