Chapter 7 - Section 7.1 - Trigonometric Identities - 7.1 Exercises - Page 543: 10

$\cos^{2}\theta(1+\tan^{2}\theta)=1$

$\cos^{2}\theta(1+\tan^{2}\theta)$ Since $1+\tan^{2}\theta=\sec^{2}\theta$, this expression becomes: $\cos^{2}\theta(1+\tan^{2}\theta)=\cos^{2}\theta\sec^{2}\theta=...$ Substitute $\sec^{2}\theta$ with $\dfrac{1}{\cos^{2}\theta}$ and simplify: $...=\cos^{2}\theta(\dfrac{1}{\cos^{2}\theta})=1$