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If $\sin^{2} θ_{1} + \sin^{2} θ_{2} + \sin^{2} θ_{3} \geq 0$ then which of the following is not the possible
value of $\cos θ_{1} + \cos θ_{2} + \cos θ_{3}$ ?

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detailed solution

Correct option is D

Let sin2θ1=sin2θ2=sin2θ3=0⇒θ1=θ2=θ3=0,π,2π⇒cosθ1=±1,cosθ2=±1,cosθ3=±1⇒cosθ1+cosθ2+cosθ3=1,-1,3,-3 but≠−2

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If sin2θ1+sin2θ2+sin2θ3≥0 then which of the following is not the possible value of cosθ1+cosθ2+cosθ3 ?

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If $\sin^{2} θ_{1} + \sin^{2} θ_{2} + \sin^{2} θ_{3} \geq 0$ then which of the following is not the possible
value of $\cos θ_{1} + \cos θ_{2} + \cos θ_{3}$ ?