Answer
$$\tan\frac{x}{2}\approx2.6456$$
Work Step by Step
$$\cos x=-0.75\hspace{2cm}\sin x\approx0.6614\hspace{2cm}\tan\frac{x}{2}\approx?$$
According to the half-angle identity for tangents:
$$\tan\frac{x}{2}=\frac{\sin x}{1+\cos x}$$
Apply the values of $\cos x$ and $\sin x$ to the formula.
$$\tan\frac{x}{2}\approx\frac{0.6614}{1-0.75}$$
$$\tan\frac{x}{2}\approx\frac{0.6614}{0.25}$$
$$\tan\frac{x}{2}\approx2.6456$$
