Trigonometric Equation involving Double Angle and Compound Angle Formula
Tag Archives: 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 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} &= […]
3 Ways of Evaluating Nested Square Roots
Nested square roots or nested radical problems are quite interesting to solve. The key skill for this question is to understand how the students can handle “…”. This enables us to set up a quadratic equation to evaluate its exact value using the quadratic formula,$$x= \frac{-b \ \pm \sqrt{b^2-4ac}}{2a}$$.Let’s look at the following examples for […]