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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

Suggest Corrections

Similar questions

Q. The possible values of

θ \in (0, π)

such that

sin (θ) + sin (4 θ) + sin (7 θ) = 0

are:

sin 7 θ + sin 4 θ + sin θ = 0, 0 < θ < \frac{π}{2}

Q. The possible values of

θ ϵ (0, π)

such that

sin (θ) + sin (4 θ) + sin (7 θ) = 0

are:

Find the sum of the possible values of $θ ϵ (0, π)$ such that $sin (θ) + sin (4 θ) + sin (7 θ) = 0$ are

T h e p o s s i b l e v a l u e s o f θ \in (0, π) s u c h t h a t sin (θ) + sin (4 θ) + sin (7 θ) = 0 a r e :

Join BYJU'S Learning Program

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