The value of
(secpi/7)+(sec3pi/7)+(sec5pi/7) is
To find the value of (sec(pi/7)) + (sec(3pi/7)) + (sec(5pi/7), we will use the trigonometric identity:
sec(x) = 1/cos(x)
First, let's find the values of cos(pi/7), cos(3pi/7), and cos(5pi/7):
cos(pi/7) is a unique value that is not easily expressible using simple fractions or commonly known values. Therefore, we can approximate it using a calculator or a math software program:
cos(pi/7) ≈ 0.62349
cos(3pi/7) can be found using the same method:
cos(3pi/7) ≈ -0.22252
cos(5pi/7) can also be found using the same method:
cos(5pi/7) ≈ -0.90097
Now that we have the values of cos(pi/7), cos(3pi/7), and cos(5pi/7), we can find their reciprocals to get the values of sec(pi/7), sec(3pi/7), and sec(5pi/7), respectively:
sec(pi/7) = 1/cos(pi/7) ≈ 1/0.62349 ≈ 1.60403
sec(3pi/7) = 1/cos(3pi/7) ≈ 1/-0.22252 ≈ -4.48107
sec(5pi/7) = 1/cos(5pi/7) ≈ 1/-0.90097 ≈ -1.11061
Finally, we can add up these values:
(sec(pi/7)) + (sec(3pi/7)) + (sec(5pi/7)) ≈ 1.60403 + (-4.48107) + (-1.11061) ≈ -4.98765
Therefore, the value of (sec(pi/7)) + (sec(3pi/7)) + (sec(5pi/7)) is approximately -4.98765.