The values of - satisfying sin 7 -sin 4 -sin- in 0-2 are

The correct option is A sin 7θ + sinθ sin 4 θ = 0 ⇒ 2 sin 4 θ.cos 3 θ sin 4 θ =0 ⇒sin 4 θ [2 cos 3 θ 1] = 0 ⇒sin 4θ = 0 or cos 3 θ = 1/2 = cos (π/3) ⇒ 4 ...

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Standard XI

Mathematics

Trigonometric Ratios of Multiples of an Angle

The values of...

Question

The values of $θ$ satisfying $sin 7 θ = sin 4 θ - sin θ$ in 0 < $θ$ < $\frac{π}{2}$ are

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Solution

The correct option is A
$sin 7 θ + sin θ - sin 4 θ = 0 \Rightarrow 2 sin 4 θ . cos 3 θ - sin 4 θ = 0 \Rightarrow sin 4 θ [2 cos 3 θ - 1] = 0$
$\Rightarrow sin 4 θ = 0 o r cos 3 θ = \frac{1}{2} = cos (\frac{π}{3}) \Rightarrow 4 θ = n π o r 3 θ = 2 n π \pm (\frac{π}{3})$
$\Rightarrow θ = \frac{n π}{4} o r θ = (\frac{2 n π}{3}) \pm (\frac{π}{9})$

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The values of θ satisfying sin7θ=sin4θ−sinθ in 0 < θ < π2 are

The correct option is A sin7θ+sinθ−sin4θ=0⇒2sin4θ.cos3θ−sin4θ=0⇒sin4θ[2cos3θ−1]=0 ⇒sin4θ=0orcos3θ=12=cos(π3)⇒4θ=nπor3θ=2nπ±(π3) ⇒θ=nπ4orθ=(2nπ3)±(π9)

The values of $θ$ satisfying $sin 7 θ = sin 4 θ - sin θ$ in 0 < $θ$ < $\frac{π}{2}$ are