Sin(30+x)cosx-cos(30+x)sin(x)=0.5

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To solve this trigonometric equation, we can use the angle addition formulas for sine and cosine:

sin(A + B) = sinAcosB + cosAsinB
cos(A + B) = cosAcosB - sinAsinB

Given equation:
sin(30+x)cosx - cos(30+x)sinx = 0.5

Applying the angle addition formulas:
sin(30)cos(x) + cos(30)sin(x) - cos(30)sin(x) + sin(30)cos(x) = 0.5

simplify:
2sin(30)*cos(x) = 0.5

We know that sin(30) = 0.5, so substitute:
2(0.5)cos(x) = 0.5
cos(x) = 0.5 / 1 = 0.5

Therefore, the solution to the equation is cos(x) = 0.5.