What is the integral of ${cos (θ)}^{2}$ $cos(theta)^2$ ?

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Answer 1 · 2016-08-13T17:52:22

$= \frac{1}{2} [ϕ + \frac{1}{2} sin 2 ϕ] + C$ $=1/2[phi + 1/2sin2phi] + C$

Use double angle formula

$cos 2 ϕ = 2 {cos}^{2} ϕ - 1$ $cos2phi = 2cos^2phi - 1$

$therefore cos^2phi = 1/2(1+cos2phi)$

$int cos^2phi dphi = 1/2 int (1+cos2phi) dphi$

$=1/2[phi + 1/2sin2phi] + C$

What is the integral of cos(theta)^2cos(θ)2 cos(theta)^2?