Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Problem Solving - Page 961: 52a

See below.

We know by our identities that $2\sin L\cos L=\sin(2L)$. Hence here $-0.014\sin L\cos L=-0.007\sin(2L)$, while the rest of the equation remains unchanged. In other words $978+5.17\sin^2L-0.014\sin L\cos L=978+5.17\sin^2L-0.007\sin(2L)$. Thus we showed what we had to.