A value of θ ∈ 0 , π 3 , for which 1 + c o s 2 θ s i n 2 θ 4   c o s 6 &#952…

A value of θ∈0,π3, for which 1+cos2θsin2θ4 cos6θcos2θ1+sin2θ4 cos6θcos2θsin2θ1+4 cos6θ=0, is
  1. π9
  2. 7π24
  3. 7π36
  4. π18

Solution

R1→R1-R2
1-10cos2θ1+sin2θ4cos6θcos2θsin2θ1+4cos6θ=0
R2→R2-R3
1-1001-1cos2θsin2θ1+4cos6θ=0
⇒1+4cos6θ+sin2θ+1cos2θ=0
1+2cos6θ=0⇒cos6θ=-12
6θ=2π3⇒θ=π9

Asked in: JEE Main 2019 (12 Apr Shift 2)

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