Question
If $\sin^2\text{x}+\sin^2\text{ x}=1,$ then write the value of $\cos^8\text{x}+2\cos^6\text{x}+\cos^4\text{ x}.$
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| Outcomes | $\omega_1$ | $\omega_2$ | $\omega_3$ | $\omega_4$ | $\omega_5$ | $\omega_6$ |
| $\frac 1{12}$ | $\frac 1{12}$ | $\frac 16$ | $\frac 16$ | $\frac 16$ | $\frac 32$ |
| Outcomes | $\omega_1$ | $\omega_2$ | $\omega_3$ | $\omega_4$ | $\omega_5$ | $\omega_6$ |
| $\frac 18$ | $\frac 23$ | $\frac 13$ | $\frac 13$ | $-\frac 14$ | $-\frac 13$ |