If $\sin32^{\circ}=k$ and $\cos x=1-2k^2, \alpha$ and $\beta$ are the two values of $x$ between $0^{\circ}$ and $360^{\circ}$ with $\alpha<\beta$

Question

A)$\alpha+\beta=180^{\circ}$

B)$\beta-\alpha=200^{\circ}$

C)$\beta=4\alpha+40^{\circ}$

D)$\beta=5\alpha-20^{\circ}$

I solved it by taking $$\cos x=1-2\sin^232^{\circ}$$

Therefore $x=64$

So the two values of $x$ can be $64$ and $334$, so B) should be the right answer, but the answer is actually c. Where am I going wrong?

Answer 1

Note that: $$\cos x=\cos 64^\circ \Rightarrow x=\pm64^\circ+ 360^\circ n \\ n=0 \Rightarrow x=64^\circ\\ n=1 \Rightarrow x=-64^\circ +360^\circ =296^\circ $$

Answer 2

$$360-64=296=\beta$$

$$4\alpha=4\cdot64=256$$