Question

What is the antiderivative of 1-cos^2(x)

Answer 1

Answer:

$\frac{1}{4}$sin2x + $\frac{1}{2}$ x + c

Step-by-step explanation:

using the trigonometric identity

• cos² x = $\frac{1}{2}$(cos2x + 1) and

∫cos ax = $\frac{1}{a}$sin ax

hence

∫(1 - $\frac{1}{2}$(cos2x + 1)dx

= ∫(1 - $\frac{1}{2}$cos2x - $\frac{1}{2}$)dx

= ∫($\frac{1}{2}$ - $\frac{1}{2}$cos2x)dx

= $\frac{1}{2}$x - $\frac{1}{4}$sin2x + c

where c is the constant of integration