prove the identity

try to Prove

cosec (π/7) = cosec(2π/7) + cosec(3π/7)

2 Answers

2305
Shaswata Roy ·

1sin(π/7) - 1sin(3π/7)

Converting the numerator into product form we get,

2cos(2π/7)sin(π/7)sin(3π/7)sin(π/7)

= 2sin(3π/14)sin(3π/7) (since cos(2π/7)= sin(3π/14))

= 2sin(3π/14)2sin(3π/14)cos(3π/14)

= 1cos(3π/14)

= 1sin(2π/7)

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

31
Gourav Bose ·

1
sin(π/7) - 1
sin(3π/7)

Converting the numerator into product form we get,

2cos(2π/7)sin(π/7)
sin(3π/7)sin(π/7)

= 2sin(3π/14)
sin(3π/7) (since cos(2π/7)= sin(3π/14))

= 2sin(3π/14)
2sin(3π/14)cos(3π/14)

= 1
cos(3π/14)

= 1
sin(2π/7)

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

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