To simplify this expression, we can use the trigonometric identities:
Given expression: 4sin(30°+a)cos(a) - 2cos(60°-2a)
= 4(sin30°cos(a) + cos30°sin(a))cos(a) - 2(cos60°cos(2a) + sin60°sin(2a))= 4[(1/2)cos(a) + (√3/2)sin(a)]cos(a) - 2[(1/2)cos(2a) + (√3/2)sin(2a)]= 2cos²(a) + 2√3sin(a)cos(a) - cos(2a) - √3sin(2a)
Therefore, the simplified expression is: 2cos²(a) + 2√3sin(a)cos(a) - cos(2a) - √3sin(2a)
To simplify this expression, we can use the trigonometric identities:
sin(A + B) = sinAcosB + cosAsinBcos(A - B) = cosAcosB + sinAsinBGiven expression: 4sin(30°+a)cos(a) - 2cos(60°-2a)
= 4(sin30°cos(a) + cos30°sin(a))cos(a) - 2(cos60°cos(2a) + sin60°sin(2a))
= 4[(1/2)cos(a) + (√3/2)sin(a)]cos(a) - 2[(1/2)cos(2a) + (√3/2)sin(2a)]
= 2cos²(a) + 2√3sin(a)cos(a) - cos(2a) - √3sin(2a)
Therefore, the simplified expression is: 2cos²(a) + 2√3sin(a)cos(a) - cos(2a) - √3sin(2a)