If sin 6 -sin 4 -sin 2 -0- then general value of - is

The correct option is A n π/4, n π±π/3, n∈ Isin 6 θ + sin 4 θ + sin 2 θ = 0 ⇒sin 4 θ + 2sin 4 θ nbsp; cos 2 θ = 0 ⇒sin 4 θ(1 + 2cos 2 θ) = 0 ⇒sin 4 θ = 0 or ...

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Standard XII

Mathematics

Trigonometric Equations

If sin 6 θ+si...

Question

If $sin 6 θ + sin 4 θ + sin 2 θ = 0,$ then general value of $θ$ is

\frac{n π}{4}, n π \pm \frac{π}{3}, n \in I

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\frac{n π}{4}, n π \pm \frac{π}{6}, n \in I

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\frac{n π}{4}, 2 n π \pm \frac{π}{3}, n \in I

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\frac{n π}{4}, 2 n π \pm \frac{π}{6}, n \in I

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Solution

The correct option is A $\frac{n π}{4}, n π \pm \frac{π}{3}, n \in I$
$sin 6 θ + sin 4 θ + sin 2 θ = 0 \Rightarrow sin 4 θ + 2 sin 4 θ cos 2 θ = 0 \Rightarrow sin 4 θ (1 + 2 cos 2 θ) = 0 \Rightarrow sin 4 θ = 0 or cos 2 θ = - \frac{1}{2} \Rightarrow 4 θ = n π or 2 θ = 2 n π \pm \frac{2 π}{3}, n \in I \Rightarrow θ = \frac{n π}{4} or θ = n π \pm \frac{π}{3}, n \in I$

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If sin 6θ+sin 4θ+sin 2θ=0, then general value of θ is

The correct option is A nπ4,nπ±π3, n∈Isin6θ+sin4θ+sin2θ=0⇒sin4θ+2sin4θcos2θ=0⇒sin4θ(1+2cos2θ)=0⇒sin4θ=0 or cos2θ=−12⇒4θ=nπ or 2θ=2nπ±2π3, n∈I⇒θ=nπ4 or θ=nπ±π3, n∈I

If $sin 6 θ + sin 4 θ + sin 2 θ = 0,$ then general value of $θ$ is