prove the identity

try to Prove

cosec (Ï€/7) = cosec(2Ï€/7) + cosec(3Ï€/7)

2 Answers

2305
Shaswata Roy ·

1sin(Ï€/7) - 1sin(3Ï€/7)

Converting the numerator into product form we get,

2cos(2Ï€/7)sin(Ï€/7)sin(3Ï€/7)sin(Ï€/7)

= 2sin(3Ï€/14)sin(3Ï€/7) (since cos(2Ï€/7)= sin(3Ï€/14))

= 2sin(3Ï€/14)2sin(3Ï€/14)cos(3Ï€/14)

= 1cos(3Ï€/14)

= 1sin(2Ï€/7)

Hence,cosec (Ï€/7) = cosec(2Ï€/7) + cosec(3Ï€/7).

31
Gourav Bose ·

1
sin(Ï€/7) - 1
sin(3Ï€/7)

Converting the numerator into product form we get,

2cos(2Ï€/7)sin(Ï€/7)
sin(3Ï€/7)sin(Ï€/7)

= 2sin(3Ï€/14)
sin(3Ï€/7) (since cos(2Ï€/7)= sin(3Ï€/14))

= 2sin(3Ï€/14)
2sin(3Ï€/14)cos(3Ï€/14)

= 1
cos(3Ï€/14)

= 1
sin(2Ï€/7)

Hence,cosec (Ï€/7) = cosec(2Ï€/7) + cosec(3Ï€/7).

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