It’s not clear if the equation is 7sin²(x)-14sin(x)+2=-5 or 7sin(2x)-14sin(x)+2=-5.

Assuming it’s the former to start with we have:

7sin²(x)-14sin(x)+7=0=7(sin²(x)-2sin(x)+1); 7(sin(x)-1)²=0.

So the solution is sin(x)=1, from which x=π/2, 5π/2, 9π/2, or, in general terms, π/2+2nπ=(4n+1)π/2 where n is any positive or negative integer, including 0. This gives x in radians. In degrees this is 90(4n+1).

This is the most likely solution and interpretation of the question.

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