Tag Archives: Double-Angle Formula

Integration using Double Angle Formula

Integration using Double Angle Formula

$$ \large \begin{align} \displaystyle\cos{2x} &= 2\cos^2{x}-1 \\&= 1-2 \sin^2 {x} \\&= \cos^2{x}-\sin^2{x} \\\sin{2x} &= 2 \sin{x} \cos{x} \end{align} $$ These will be expressed in the following forms to apply to integration. $$ \large \begin{align} \displaystyle\sin^2 x &= \dfrac{1}{2}(1-\cos 2x) \\\cos^2 x &= \dfrac{1}{2}(1 + \cos 2x) \\\sin x \cos x &= \dfrac{1}{2} \sin 2x \end{align} […]

Integrating Trigonometric Functions by Double Angle Formula

Integrating Trigonometric Functions by Double Angle Formula

Integrating Trigonometric Functions by Double Angle Formula Integrating Trigonometric Functions can be done by Double Angle Formula reducing the power of trigonometric functions. \( \begin{aligned} \displaystyle\cos{2A} &= 2\cos^2{A}-1 \\&= 1-2\sin^2{A} \\&= \cos^2{A}-\sin^2{A} \end{aligned} \) Practice Questions Question 1 Find \( \displaystyle \int{\cos^2{x}}dx \). \( \begin{aligned} \displaystyle2\cos^2{x}-1 &= \cos{2x} \\2\cos^2{x} &= \cos{2x} + 1 \\\cos^2{x} &= […]