code: def TR15(rv, max=4, pow=False):
      """Convert sin(x)**-2 to 1 + cot(x)**2.
  
      See _TR56 docstring for advanced use of ``max`` and ``pow``.
  
      Examples
      ========
  
      >>> from sympy.simplify.fu import TR15
      >>> from sympy.abc import x
      >>> from sympy import sin
      >>> TR15(1 - 1/sin(x)**2)
      -cot(x)**2
  
      """
  
      def f(rv):
          if not (isinstance(rv, Pow) and isinstance(rv.base, sin)):
              return rv
  
          e = rv.exp
          if e % 2 == 1:
              return TR15(rv.base ** (e + 1)) / rv.base
  
          ia = 1 / rv
          a = _TR56(ia, sin, cot, lambda x: 1 + x, max=max, pow=pow)
          if a != ia:
              rv = a
          return rv
  
      return bottom_up(rv, f)
  
imports: from collections import defaultdict
  from sympy.core.add import Add
  from sympy.core.expr import Expr
  from sympy.core.exprtools import Factors, gcd_terms, factor_terms
  from sympy.core.function import expand_mul
  from sympy.core.mul import Mul
  from sympy.core.numbers import pi, I
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.core.sorting import ordered
  from sympy.core.symbol import Dummy
  from sympy.core.sympify import sympify
  from sympy.core.traversal import bottom_up
  from sympy.functions.combinatorial.factorials import binomial
  from sympy.functions.elementary.hyperbolic import cosh, sinh, tanh, coth, sech, csch, HyperbolicFunction
  from sympy.functions.elementary.trigonometric import cos, sin, tan, cot, sec, csc, sqrt, TrigonometricFunction
  from sympy.ntheory.factor_ import perfect_power
  from sympy.polys.polytools import factor
  from sympy.strategies.tree import greedy
  from sympy.strategies.core import identity, debug
  from sympy import SYMPY_DEBUG
label_desc: Use image node_id 22 for calling a global function with example usage: TR15(rv, max, pow) and returns: bottom_up, rv, rv, unknown