If 4 sin 2-1- then the value of - are-

The correct option is B nπ±π/6,n ∈ Z Given: ⇒ 4 sin^2θ=1 ⇒ sin^2θ=1/4 ⇒ sinθ=1/2 or sin θ= 1/2 ⇒ sinθ=π/6or sinθ=sin ( π/6 ) ⇒θ=nπ+( 1)^nπ/6,n ∈ Z or θ =n π ...

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Byju's Answer

Standard XII

Mathematics

General Solution of Trigonometric Equation

If 4 sin 2θ=1...

Question

$I f 4 s i n^{2} θ = 1, t h e n t h e v a l u e o f θ a r e .$

$2 n π \pm \frac{π}{3}, n \in Z$

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$n π \pm \frac{π}{3}, n \in Z$

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$n π \pm \frac{π}{6}, n \in Z$

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$2 n π \pm \frac{π}{6}, n \in Z$

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Solution

The correct option is C
$n π \pm \frac{π}{6}, n \in Z$

$G i v e n : \Rightarrow 4 s i n^{2} θ = 1 \Rightarrow s i n^{2} θ = \frac{1}{4} \Rightarrow s i n θ = \frac{1}{2} o r s i n θ = - \frac{1}{2} \Rightarrow s i n θ = \frac{π}{6} o r s i n θ = s i n (- \frac{π}{6}) \Rightarrow θ = n π + (- 1)^{n} \frac{π}{6}, n \in Z o r θ = n π + (- 1)^{n} (- \frac{π}{6}), n \in Z \Rightarrow θ = n π \pm \frac{π}{6}, n \in Z$

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Q. If

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(b)

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(c)

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If 4 sin2θ=1,then the value of θ are.

The correct option is C nπ±π6,n∈Z Given:⇒4 sin2θ=1⇒sin2θ=14⇒sinθ=12 or sin θ=−12⇒sinθ=π6or sinθ=sin(− π6)⇒θ=nπ+(−1)nπ6,n∈Z or θ =nπ+(−1)n(− π6),n∈Z⇒θ=nπ±π6,n∈Z

$I f 4 s i n^{2} θ = 1, t h e n t h e v a l u e o f θ a r e .$