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Question

The value(s) of θ, which satisfy 32cosθ4sinθcos2θ+sin2θ=0 is/are

A
θ=2nπ;nI
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B
2nπ+π2;nI
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C
2nππ2;nI
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D
nπ;nI
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Solution

The correct options are
C 2nπ+π2;nI
D θ=2nπ;nI

32cosθ4sinθcos2θ+sin2θ=0
sin2θ2cosθ+34sinθ(12sin2θ)=0
2cosθ(sinθ1)+2sin2θ4sinθ+2=0
2cosθ(sinθ1)+2(sinθ1)2=0
Or
2(sinθ1)(cosθ+sinθ1)=0
sinθ=1
Or
θ=2nπ+π2.
And
cosθ+sinθ1=0
Or
2[sin(θ+π4)]=1
Or
sin(θ+π4)=12
Or
θ+π4=2nπ+π4
Or θ=2nπ.


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