Question: Show detailed steps on these five following problems (i.e., how you got to your answer).

a) \({{\sec }^{2}}x\cot x-\cot x=\tan x\)

b) \(\frac{1}{\tan \theta \csc \theta }=\cos \theta \)

c) \({{\left( \sin x+\cos x \right)}^{2}}=1+\sin 2x\)

d) \(\cos \theta \csc \theta =\cot \theta \)

e) \(\frac{1}{\sec x+1}-\frac{1}{\sec x-1}=-2{{\cot }^{2}}x\)