Question

[Precalculus] Simplify:

Answer 1

Numerator:

Apply the definition of secant and cotangent:

`\sec(x) = (1)/(\cos(x)),\ \cot(x) = (\cos(x))/(\sin(x))`

So, their product is

`(1)/(\cos(x)) * (\cos(x))/(\sin(x)) = (1)/(\sin(x)) = \csc(x)`

Denominator:

Simply factor a 2 and use the fundamental trigonometric identity:

`2\cos^2(x)+2\sin^2(x) = 2(\cos^2(x)+\sin^2(x)) = 2* 1 = 2`

So, the answer is

`(\csc(x))/(2)`