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Let f(θ)=cot⁡θ1−tan⁡θ+tan⁡θ1−cot⁡θ,π<θ<3π4 , then f9π8 is equal to

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a

1+2

b

1+22

c

2−1

d

22−1

answer is B.

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Detailed Solution

f(θ)=1tan⁡θ1(1−tan⁡θ)+tan⁡θ⋅tan⁡θtan⁡θ−1=1−tan3⁡θtan⁡θ(1−tan⁡θ)=1+tan⁡θ+tan2⁡θtan⁡θ=1+2sin⁡2θ∴f9π8=1+2sin⁡9π4=1+22

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