4cosasina+cos^2(a)
To simplify the given expression, 4cos(a) + cos^2(a), we can start by factoring out a common factor, which is cos(a):
cos(a)(4 + cos(a))
Since we cannot simplify the expression further, this is the simplified form of the given expression: cos(a)(4 + cos(a)).
To simplify the expression 4cos(a) + cos^2(a), we can substitute cos^2(a) with its equivalent using the identity cos^2(a) = 1 - sin^2(a):
4cos(a) + cos^2(a) = 4cos(a) + 1 - sin^2(a)
Now, let's focus on the term sin^2(a). To simplify this term, we can use the Pythagorean identity sin^2(a) + cos^2(a) = 1. By rearranging this identity, we can solve for sin^2(a):
sin^2(a) = 1 - cos^2(a)
Substituting this back into the original expression:
4cos(a) + cos^2(a) = 4cos(a) + 1 - (1 - cos^2(a))
Now, we can simplify further:
4cos(a) + cos^2(a) = 4cos(a) + 1 - 1 + cos^2(a)
Combine like terms:
4cos(a) + cos^2(a) = 4cos(a) + cos^2(a)
Therefore, the simplified expression is 4cos(a) + cos^2(a).