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Q.

Let f(θ)=tan3⁡θ1+tan2⁡θ−cot3⁡θ1+cot2⁡θ,0<θ<π4 Then f (θ)  is equal to

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a

tan⁡θ+cot⁡θ

b

2sin⁡(2θ)

c

−2cot⁡(2θ)

d

0

answer is C.

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Detailed Solution

f(θ)=sin3⁡θcos⁡θ−cos3⁡θsin⁡θ=sin4⁡θ−cos4⁡θcos⁡θsin⁡θ−−cos2⁡θ−sin2⁡θ(1)cos⁡θsin⁡θ=−2cot⁡(2θ)
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