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