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Sloan [31]
3 years ago
7

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

Mathematics
1 answer:
Alex17521 [72]3 years ago
3 0
Main formula cos (a - b) =cosacosb + sina sinb
arccos(-x) = pi -arccosx

<span>cos x cos (pi/7)+sin x sin(pi/7) = cos(x-pi/7)

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

</span>arc cos[(sqrt 2)/2 ] = Pi/4 + 2kpi, and then x -pi/7 = pi - pi/4 +2kpi,
 implies x= -pi/7 + pi - pi/4 = -<span>pi/7 + 3pi/4 = -19pi/28 + 2kpi</span>
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