irinan2014

Verified answer

Всё подробно написала в решении.

oganesbagoyan

Verified answer

7 ^(cos(2x -π/2)) =49^(cosx) ; x∈[ -2;4].
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7 ^(cos(2x -π/2)) =7^(2cosx) ;
cos(2x -π/2) =2cosx ;
cos(π/2 -2x) =2cosx ;
sin2x =2cosx ;
2sinxcosx = 2cosx ;
2cosx (sinx -1)= 0 ;
[cosx =0 ; sinx -1= 0 ⇒[x=π/2 +πn ; x =π/2+2πn ;n∈Z.
 x∈[ -2;4] ⇒x₁ = - π/2 ;  x₂ = π/2 .
 
ответ : x₁ = - π/2 ;  x₂ = π/2 .