If cos x cos (pi/7) + sin x sin (pi/7) = - (sqrt 2) / 2, then x can equal

Question

Mathematics

Korbin Cummings

12 August, 07:43

If cos x cos (pi/7) + sin x sin (pi/7) = - (sqrt 2) / 2, then x can equal

+3

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Dewey · Answer 1

Main formula cos (a - b) = cosacosb + sina sinb

arccos (-x) = pi - arccosx

cos x cos (pi/7) + sin x sin (pi/7) = cos (x-pi/7)

so cos (x-pi/7) = - (sqrt 2) / 2, x - pi/7 = arc cos[ - (sqrt 2) / 2 ] = pi - arc cos[ (sqrt 2) / 2 ]

arc cos[ (sqrt 2) / 2 ] = Pi/4 + 2kpi, and then x - pi/7 = pi - pi/4 + 2kpi,

implies x = - pi/7 + pi - pi/4 = - pi/7 + 3pi/4 = - 19pi/28 + 2kpi