What can I conclude from this inequality? I was solving an equation and reached this inequality
$$t^2−1≤\sin^2\alpha$$

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*What conclusions can I draw about $t$ from the above inequality (given that $\alpha \in \mathbb R$)?


*Is it correct to use the minimum value of RHS (zero) and proceed?
Here's the complete context of the question:


Since the minimum value of $\sin^2 \alpha$ is $0$, this means that for any real $t$ in $-1 ≤ t ≤ 1$, the inequality will hold regardless of the value of $\alpha$.
Similarly, the maximum value of $\sin^2 \alpha$ is $1$. This means that for any $t$ that satisfy $t < -\sqrt{2}$ or $t > \sqrt{2}$, the inequality will not hold regardless of $\alpha$.
Now you can relate this back to the range of the function.
