Question : Simplify the following:
$\frac{\cos x-\sqrt{3} \sin x}{2}$

Option 1: $\cos \left(\frac{\pi}{3}-x\right)$

Option 2: $\sin \left(\frac{\pi}{3}+x\right)$

Option 3: $\cos \left(\frac{\pi}{3}+x\right)$

Option 4: $\sin \left(\frac{\pi}{3}-x\right)$

Question : Simplify the following.
$\frac{\sin^3 \alpha+\cos^3 \alpha}{\sin \alpha+\cos \alpha}$

Option 1: $1+\sin \alpha \cos \alpha$

Option 2: $\tan \alpha$

Option 3: $1-\sin \alpha \cos \alpha$

Option 4: $\sec \alpha$

Question : Simplify the following expression.
$\frac{\sin \theta - 2 \sin ^3 \theta}{2 \cos ^3 \theta - \cos \theta}$

Option 1: $\tan \theta$

Option 2: $\sin \theta$

Option 3: $\sec \theta$

Option 4: $\cos \theta$

Question : If $\cos x+\sin x=\sqrt{2} \cos x$, what is the value of $(\cos x-\sin x)^2+(\cos x+\sin x)^2$?

Option 1: $2$

Option 2: $1$

Option 3: $0$

Option 4: $\frac{1}{\sqrt{2}}$

Question : Simplify the given expression.
$\frac{1+\sin^4 \theta+\cos^4 \theta}{\cos^2 \theta+\sin^4 \theta}$

Option 1: 3

Option 2: 1

Option 3: 2

Option 4: 4