2sin((3p/2)-x)cos((p/2)-x)=sqrt(2)cosx. Created by 88xx88. algebra-ru

2)-x)=sqrt(2)cosx...

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2sin((3p/2)-x)cos((p/2)-x)=sqrt(2)cosx

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oganesbagoyan

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2sin(3π/2 -x)*cos(π/2 -x) =√2 *cosx ;
-2cosx*sinx = √2 *cosx ;
2 cosx*sinx + √2 *cosx =0  ;
2 cosx*(sinx + √2 / 2) = 0 ;

a)  cosx = 0 ⇒x =π/2 +π*n , n∈Z .
b) sinx + √2 / 2 =0 ;
sinx = - √2 / 2   ;
x = (-1)^(n+1)* (π/4) +π*n , n∈Z ..

ответ   : { π/2 +π*n ;   (-1)^(n+1)* (π/4) +π*n  , n∈Z }

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