TRIG_TR1

This transformation rewrites reciprocal trigonometric functions into explicit reciprocal forms built from sine and cosine.

It applies identities:

\sec(x)=\frac{1}{\cos(x)},\quad \csc(x)=\frac{1}{\sin(x)}

This normalized form can make further simplification steps easier.

Excel Usage

=TRIG_TR1(expression)

• expression (str, required): Expression containing sec and csc terms (expression string).

Returns (str): Transformed expression as a string, or an error message.

Example 1: Rewrites secant to reciprocal cosine

Inputs:

expression
sec(x)

Excel formula:

=TRIG_TR1("sec(x)")

Expected output:

"1/cos(x)"

Example 2: Rewrites cosecant to reciprocal sine

Inputs:

expression
csc(x)

Excel formula:

=TRIG_TR1("csc(x)")

Expected output:

"1/sin(x)"

Example 3: Rewrites mixed secant and cosecant sum

Inputs:

expression
2*csc(x) + sec(x)

Excel formula:

=TRIG_TR1("2*csc(x) + sec(x)")

Expected output:

"1/cos(x) + 2/sin(x)"

Example 4: Rewrites reciprocal functions in nested expression

Inputs:

expression
sec(x + y) + csc(x - y)

Excel formula:

=TRIG_TR1("sec(x + y) + csc(x - y)")

Expected output:

"1/cos(x + y) + 1/sin(x - y)"

Python Code

from sympy import sympify
from sympy.simplify.fu import TR1 as sympy_tr1

def trig_tr1(expression):
    """
    Rewrite secant and cosecant into reciprocal cosine and sine forms.

    See: https://docs.sympy.org/latest/modules/simplify/fu.html#sympy.simplify.fu.TR1

    This example function is provided as-is without any representation of accuracy.

    Args:
        expression (str): Expression containing sec and csc terms (expression string).

    Returns:
        str: Transformed expression as a string, or an error message.
    """
    try:
        expr_text = expression.replace("^", "**") if isinstance(expression, str) else expression
        expr_obj = sympify(expr_text)
        result = sympy_tr1(expr_obj)
        return str(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

expression *

Expression containing sec and csc terms (expression string).