Mathematics

Problem

Consider the expression

E=\dfrac{\sec 30^{\circ}-\cot 60^{\circ}}{1+\csc 30^{\circ}}

. a. (i) Re-express each trigonometric term in

E

using

\sin\theta

\cos\theta

only. b. (ii) Substitute the exact values of

\sin 30^{\circ},\;\cos 30^{\circ},\;\sin 60^{\circ}

and

\cos 60^{\circ}

to evaluate

E

. c. (iii) Simplify your answer to obtain the final numerical value of

E