Chapter 8 - Applications of Trigonometric Functions - 8.1 Right Triangle Trigonometry; Applications - 8.1 Assess Your Understanding - Page 519: 23

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The identity says: $\sin^2{(\theta)}+\cos^2{(\theta)}=1$. We also know that $\sin{(\theta)}=\cos{(90^{o}-\theta)}$, hence $1-\cos^2{(20^{o})}-\cos^2{(70^{o})}=1-\cos^2{(20^{o})}-\sin^2{(20^{o})}=1-(\cos^2{(20^{o})}+\sin^2{(20^{o}))}=1-1=0.$