To solve this trigonometric equation, we can use the angle addition formulas for sine and cosine:
sin(A + B) = sinAcosB + cosAsincos(A + B) = cosAcosB - sinAsinB
Given equationsin(30+x)cosx - cos(30+x)sinx = 0.5
Applying the angle addition formulassin(30)cos(x) + cos(30)sin(x) - cos(30)sin(x) + sin(30)cos(x) = 0.5
simplify2sin(30)*cos(x) = 0.5
We know that sin(30) = 0.5, so substitute2(0.5)cos(x) = 0.cos(x) = 0.5 / 1 = 0.5
Therefore, the solution to the equation is cos(x) = 0.5.
To solve this trigonometric equation, we can use the angle addition formulas for sine and cosine:
sin(A + B) = sinAcosB + cosAsin
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.
cos(x) = 0.5 / 1 = 0.5
Therefore, the solution to the equation is cos(x) = 0.5.