Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 204: 95c

$E(t) = 3$

We can use the following fundamental identity: $cos^2~x+sin^2~x = 1$ $L(t) = 3cos^2(6,000,000~t)$ $C(t) = 3sin^2(6,000,000~t)$ We can derive a simplified expression for $E(t)$: $E(t) = L(t)+C(t)$ $E(t) = 3cos^2(6,000,000~t)+3sin^2(6,000,000~t)$ $E(t) = 3~[cos^2(6,000,000~t)+sin^2(6,000,000~t)]$ $E(t) = 3~(1)$ $E(t) = 3$