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simplify: (2sin(2pie/7))/(3cos(3pie/14)

2 answers

what's he problem. Got no calculator?

sin 2pi/7 = .7818
cos 3pi/14 = .7818

so, 2/3

Note that 2pi/7 + 3pi/14 = pi/2
recall that sinA = cos(π/2 -A)

(2sin(2pie/7))/(3cos(3pie/14)
= 2cos(π/2 - 2π/7) / 3cox(3π/14)
= 2cos(3π/14) / 3cos(3π/14)
= 2/3
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