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is x=15 degrees a solution of radical 3/3 cos2x+sin2x=0

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By radical 3 do you mean the cube root of (3 cos2x+sin2x) ?

Do you mean cos^2 x and sin^2 x or cos (2x) and sin (2x)?

The cube root will be zero if and only if 3cos2x+sin2x is also zero. Put in 15 degrees for x and see what you get.
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