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Question

The value of θ satisfying ∣ ∣11sin3θ43cos2θ772∣ ∣=0 in [0,2π] is

A
5
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B
5.00
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C
5.000
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D
5.0
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Solution

We have
∣ ∣11sin3θ43cos2θ772∣ ∣=0
Applying C1C1+C2, we get
∣ ∣21sin3θ13cos2θ072∣ ∣=0
Applying R1R1+2R2
∣ ∣07sin3θ+2cos2θ13cos2θ072∣ ∣=0
Expanding along C1, we get
=1[14+7(sin3θ+2cos2θ]=0
(3sinθ4sin3θ)+2(12sin2θ)2=04sin3θ+4sin2θ3sinθ=0sinθ(4sin2θ+4sinθ3)=0sinθ(4sin2θ+6sinθ2sinθ3)=0sinθ(2sinθ1)(2sinθ+3)=0sinθ=0 or sinθ=12 or sinθ=32
sinθ32
sinθ=0 or 12
Possible values of θ=0,π,2π,π6,5π6

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