Question

question 7
\frac{\sin^{2}x + \cos^{2}x}{\cos^{2}x}

Explanation:

Step1: Split the fraction

$$\frac{\sin^{2}x+\cos^{2}x}{\cos^{2}x}=\frac{\sin^{2}x}{\cos^{2}x}+\frac{\cos^{2}x}{\cos^{2}x}$$

Step2: Use trigonometric identities

Since $\frac{\sin x}{\cos x}=\tan x$ and $\frac{\cos^{2}x}{\cos^{2}x} = 1$, we get $\tan^{2}x + 1$.
Also, from the Pythagorean identity $1+\tan^{2}x=\sec^{2}x$

Answer:

$\sec^{2}x$