Решите за 30 баллов ( с объяснением) sin(x+30)+cos(x+60)=1+cos2x

Task/27400429
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Решите sin(x+30)+cos(x+60 ) =1+cos2x
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cos(x+60°)+sin(x+30°) =1+cos2x ;
1 способ
cosx*cos60° — sinx*sin60° +sinx*cos30° +cosx*sin30° =1+cos2x ;
(1/2)*cosx -(v3 /2 )sinx + sinx* (v3 /2 ) +cosx*(1/2) =2cos?x ;
cosx = 2cos?x ;
2cosx (cosx -1/2)= 0  ;
cosx =0 ? x =?/2+?n, n ?Z .
или
cosx -1/2=0 ?cosx =1/2 ? x = ±?/3 +2?k , k  ? Z.

ответ: ?/2+?n ,n ?Z ;  ±?/3 +2?k , k  ? Z.
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2 способ
cos(x+60°)+ cos(90° -(x+30°) ) =1+cos2x ;
cos(x+60°)  +cos(60°- x) =1+cos2x ;
2cos60°*cosx =2cos?x ;
cosx = 2cos?x ;
… дальше как в 1 способе
* * * * * * * P.S. * * * * * * *
cos(?+?) =cos?cos? — sin?sin? ;
sin(?+?) =sin?cos? + cos?sin? ;
cos2x =cos?x -sin?x = 2cos?x — 1?1+cos2x =2cos?x ;.
cos(90° — ?) =sin?
cos?+cos?= 2cos(?+?)/2 *cos(?-?)/2 .