6sin^2x+5sin(p/2-x)-2=0

Question

6sin^2x+5sin(p/2-x)-2=0

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Сделаете полное решение

Answer 1

6 sin^2 x + 5 sin (p/2 - x)  - 2 = 0;
 sin^2 x = 1 - cos^2 x ;
sin (p/2 - x ) = cos x; 
6(1 - cos^2 x) + 5 cos x - 2 = 0;
6 - 6 cos^2 x + 5 cos x - 2 = 0;
6 cos^2 x - 5 cos x - 4 = 0;
 D = 25 + 96 = 121= 11^2;
 cos x = 4/3 > 1; ∅;
 cos x = - 1/2;
 x = + - p/3  + 2pk;k-Z