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Question

The smallest value of (θ) satisfying the equation 3 (cotθ+tanθ) = 4 is


A

2 π/3

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B

π/3

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C

π/6

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D

π/12

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Solution

The correct option is C

π/6


Given:3(cotθ+tan θ)=43(cosθsinθ+sinθcosθ)3(cos2 θ+sin2 θ)=4 sinθ cosθ3=2 sin 2θ[sin2θ=2 sinθ cosθ]sin 2θ=32sin 2θ=sinπ22θ=nπ+(1)nπ3,nZθ=nπ2+(1)nπ6,nZTo obrain the smallest value ofθ,we will put n=0 in the above equation.Thus,we have,θ=π6Hence,the smallest value ofθ is π6.


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