TRIG_TR7

This transformation lowers cosine-squared terms to first-degree cosine at double angle using a power-reduction identity.

The identity used is:

\cos^2(x)=\frac{1+\cos(2x)}{2}

This is useful when preparing expressions for integration, simplification, or harmonics analysis.

Excel Usage

=TRIG_TR7(expression)

• expression (str, required): Expression containing cosine-squared terms (expression string).

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

Example 1: Reduces cosine squared to double-angle form

Inputs:

expression
cos(x)^2

Excel formula:

=TRIG_TR7("cos(x)^2")

Expected output:

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

Example 2: Reduces cosine squared inside additive expression

Inputs:

expression
cos(x)^2 + 1

Excel formula:

=TRIG_TR7("cos(x)^2 + 1")

Expected output:

"cos(2*x)/2 + 3/2"

Example 3: Reduces scaled cosine squared term

Inputs:

expression
3*cos(a)^2

Excel formula:

=TRIG_TR7("3*cos(a)^2")

Expected output:

"3*cos(2*a)/2 + 3/2"

Example 4: Reduces multiple cosine squared terms

Inputs:

expression
cos(x)^2 + cos(y)^2

Excel formula:

=TRIG_TR7("cos(x)^2 + cos(y)^2")

Expected output:

"cos(2*x)/2 + cos(2*y)/2 + 1"

Python Code

from sympy import sympify
from sympy.simplify.fu import TR7 as sympy_tr7

def trig_tr7(expression):
    """
    Apply power-reduction to cosine-squared terms.

    See: https://docs.sympy.org/latest/modules/simplify/fu.html#sympy.simplify.fu.TR7

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

    Args:
        expression (str): Expression containing cosine-squared 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_tr7(expr_obj)
        return str(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

expression *

Expression containing cosine-squared terms (expression string).