The most general values of θ satisfying the equation $$(1+2sin$$θ$$)2+(3tan$$θ−$$1)2=0$$ are given by

Correct option is 32nπ+7π6,n∈z

Questions

The most general values of $θ$ satisfying the equation ${(1 + 2 \sin θ)}^{2} + {(\sqrt{3} \tan θ - 1)}^{2} = 0$ are given by

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nπ+π6,n∈z

nπ2+(−1)n7π6

2nπ+7π6,n∈z

2nπ+11π4,n∈z

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detailed solution

Correct option is C

sum of squares =0 ⇒each term=01+2 sinθ=0 ⇒sinθ=−12, 3tanθ−1=0 ⇒ tanθ=13 ∴ θ∈θ3 then θ = 2nπ+7π6

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The most general values of θ satisfying the equation (1+2sinθ)2+(3tanθ−1)2=0 are given by

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The most general values of $θ$ satisfying the equation ${(1 + 2 \sin θ)}^{2} + {(\sqrt{3} \tan θ - 1)}^{2} = 0$ are given by