Numerator:
Apply the definition of secant and cotangent:
[tex] \sec(x) = \dfrac{1}{\cos(x)},\ \cot(x) = \dfrac{\cos(x)}{\sin(x)} [/tex]
So, their product is
[tex] \dfrac{1}{\cos(x)} \times \dfrac{\cos(x)}{\sin(x)} = \dfrac{1}{\sin(x)} = \csc(x) [/tex]
Denominator:
Simply factor a 2 and use the fundamental trigonometric identity:
[tex] 2\cos^2(x)+2\sin^2(x) = 2(\cos^2(x)+\sin^2(x)) = 2\times 1 = 2 [/tex]
So, the answer is
[tex] \dfrac{\csc(x)}{2} [/tex]
