\[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]

↓

\[\frac{\frac{\cos \left(2 \cdot x\right)}{\left(cos \cdot x\right) \cdot sin}}{\left(cos \cdot x\right) \cdot sin}\]

Error

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Initial program 27.1
\[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]
Initial simplification2.8
\[\leadsto \frac{\cos \left(2 \cdot x\right)}{\left(sin \cdot \left(x \cdot cos\right)\right) \cdot \left(sin \cdot \left(x \cdot cos\right)\right)}\]
Using strategy rm
Applied associate-/r*2.5
\[\leadsto \color{blue}{\frac{\frac{\cos \left(2 \cdot x\right)}{sin \cdot \left(x \cdot cos\right)}}{sin \cdot \left(x \cdot cos\right)}}\]
Final simplification2.5
\[\leadsto \frac{\frac{\cos \left(2 \cdot x\right)}{\left(cos \cdot x\right) \cdot sin}}{\left(cos \cdot x\right) \cdot sin}\]

herbie shell --seed 2018219 
(FPCore (x cos sin)
  :name "cos(2*x)/(cos^2(x)*sin^2(x))"
  (/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x))))