Question 1

Evaluate the following :

(i) $\sin 60^\circ \cos 30^\circ + \sin 30^\circ \cos 60^\circ$

(ii) $2 \tan^2 45^\circ + \cos^2 30^\circ - \sin^2 60^\circ$

(iii) $\dfrac{\cos 45^\circ}{\sec 30^\circ} + \csc 30^\circ$

(iv) $\dfrac{\sin 30^\circ + \tan 45^\circ - \csc 60^\circ}{\sec 30^\circ + \cos 60^\circ + \cot 45^\circ}$

(v) $\dfrac{2 \sin 60^\circ + 5 \cos 60^\circ}{4 \sec 30^\circ - \tan 45^\circ} + \dfrac{\sin 30^\circ}{\cos 30^\circ}$