Evaluate the following trigonometric expressions: 1 sec(30°) 2 cos(60°) + tan(45°) 3 cos(30°) * sin(60°) 4 sin(60°)cos(30°) - cos(60°)sin(30°) 5 sin(45°)

$$\sec 30^\circ = \frac{1}{\cos 30^\circ}$$ $$\cos 30^\circ = \frac{\sqrt{3}}{2}$$

$$\sec 30^\circ = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$$

The value is $\boxed{\frac{2\sqrt{3}}{3}}$.

$$\cos 60^\circ = \frac{1}{2}$$ $$\tan 45^\circ = 1$$

$$\cos 60^\circ + \tan 45^\circ = \frac{1}{2} + 1 = \frac{3}{2}$$

The value is $\boxed{\frac{3}{2}}$.

$$\cos 30^\circ = \frac{\sqrt{3}}{2}$$ $$\sin 60^\circ = \frac{\sqrt{3}}{2}$$

$$\cos 30^\circ \times \sin 60^\circ = \frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} = \frac{3}{4}$$

The value is $\boxed{\frac{3}{4}}$.

$$\sin A \cos B - \cos A \sin B = \sin(A-B)$$

Here, $A = 60^\circ$ and $B = 30^\circ$.

$$\sin 30^\circ = \frac{1}{2}$$

The value is $\boxed{\frac{1}{2}}$.

$$\sin^2 \theta + \cos^2 \theta = 1$$

Here, $\theta = 45^\circ$.

$$\sin^2 45^\circ + \cos^2 45^\circ = 1$$

The value is $\boxed{1}$.

Since $30^\circ$ is in the first quadrant, $\cos 30^\circ$ is positive.

$$\sqrt{\cos^2 30^\circ} = \cos 30^\circ$$

$$\cos 30^\circ = \frac{\sqrt{3}}{2}$$

The value is $\boxed{\frac{\sqrt{3}}{2}}$.

Assuming "cos ec60" means $\csc 60^\circ$.

$$\csc 60^\circ = \frac{1}{\sin 60^\circ} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$$ $$\tan 45^\circ = 1$$ $$\sin 30^\circ = \frac{1}{2}$$ $$\sec 30^\circ = \frac{1}{\cos 30^\circ} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$$

$$\frac{\frac{2\sqrt{3}}{3} \cdot \frac{1}{2}}{\frac{2\sqrt{3}}{3}} = \frac{1}{2}$$

The value is $\boxed{\frac{1}{2}}$.