Mathematics

Problem

Let

E=\dfrac{\sec x-\cos x}{\csc x+\sin x}

. a. (i) Simplify

E

so that the final answer contains only

\tan x

. b. (ii) Using the simplified form, calculate the numerical value of

E

when

x=45^{\circ}

. State any restrictions on

x

for which

E

is not defined.