Question$$5$$
Show that $(\sec x+\cos x)^{2}$ can be expressed as $\sec ^{2} x+a+b \cos 2 x$, where $a$ and $b$ are constant to be determined.

Studdy Solution
Identify the constants $a$ and $b$ in the expression $\sec^2 x + a + b \cos 2x$.
Comparing $\sec^2 x + \frac{5}{2} + \frac{\cos 2x}{2}$ with $\sec^2 x + a + b \cos 2x$, we find:
$$a = \frac{5}{2}$$ $$b = \frac{1}{2}$$
Thus, the expression $(\sec x + \cos x)^2$ can be written as $\sec^2 x + \frac{5}{2} + \frac{1}{2} \cos 2x$.