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Question: If \(\sin 3 \theta = \sin \theta\) then the general value of \(\theta\) is...

If sin⁡3θ=sin⁡θ\sin 3 \theta = \sin \theta then the general value of θ\theta is

A

2nπ,(2n+1)π32 n \pi , ( 2 n + 1 ) \frac { \pi } { 3 }

B

nπ,(2n+1)π4n \pi , ( 2 n + 1 ) \frac { \pi } { 4 }

C

nπ,(2n+1)π3n \pi , ( 2 n + 1 ) \frac { \pi } { 3 }

D

None of these

Answer

nπ,(2n+1)π4n \pi , ( 2 n + 1 ) \frac { \pi } { 4 }

Explanation

Solution

sin⁡3θ=sin⁡θ\sin 3 \theta = \sin \theta or 3θ=mπ+(−1)mθ3 \theta = m \pi + ( - 1 ) ^ { m } \theta

For (m) even i.e., m=2nm = 2 n then θ=2nπ2=nπ\theta = \frac { 2 n \pi } { 2 } = n \pi

And for (m) odd, i.e., m=(2n+1)m = ( 2 n + 1 ) then θ=(2n+1)π4\theta = ( 2 n + 1 ) \frac { \pi } { 4 }