Integration using Trigonometric Properties

Trigonometric properties such as the sum of squares of sine and cosine with the same angle is one,
$$ \displaystyle \sin^2{\theta} + \cos^2{\theta} = 1 \\
\cos\Big(\frac{\pi}{2} – \theta \Big) = \sin{\theta} $$
can simplify harder integration.

Worked Example of Integration using Trigonometric Properties

(a)    Find \(a\) and \(b\) for \(\displaystyle \frac{1}{x(4-x)} = \frac{a}{x} + \frac{b}{4-x} \).


(b)    Evaluate \(\displaystyle A =\int_{1}^{3}\frac{\cos^2{\ddfrac{\pi x}{8}}}{x(4-x)} dx \).

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