The positive integer value of n> 3 satisfying the equation 1sin⁡πn=1sin⁡2πn+1sin⁡3πn is

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answer is 7.

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Detailed Solution

1sin⁡πn−1sin⁡3πn=1sin⁡2πn⇒sin⁡3πn−sin⁡πnsin⁡πnsin⁡3πn=1sin⁡2πn⇒2sin⁡πncos⁡2πnsin⁡2πnsin⁡πnsin⁡3πn=1⇒sin⁡4πn=sin⁡3πn⇒4πn+3πn=π⇒n=7

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