9)

let $u=x^2$

$\sin(u)=\dfrac 1 2$ for $-\pi \leq u \leq \pi$

can you solve that? There are two solutions in between $-\pi$ and $\pi$. You should be able to solve that.

Then solve $u=x^2$ This will give you 4 solutions total.

10)

hint: $1+\tan^2(x)=\sec^2(x)$

2nd hint: (you shouldn't need this one) $\cos^4(x)=\left(\cos^2(x)\right)^2=\left(1-sin^2(x)\right)^2$

11)

$\dfrac 1 {\cos(\theta)}+\tan(\theta)=\dfrac{1+\sin(\theta)} {cos(\theta)}$

Now multiply that by $1$ in the form of $\dfrac{1-\sin(\theta)}{1-\sin(\theta)}$ and simplify it.