Python | sympy.trigsimp() method

With the help of sympy.trigsimp() method, we can simplify mathematical expressions using trigonometric identities.

Syntax: trigsimp(expression) Parameters: expression – It is the mathematical expression which needs to be simplified. Returns: Returns a simplified mathematical expression corresponding to the input expression.

Example #1: In this example, we can see that by using sympy.trigsimp() method, we can simplify any mathematical expression. 

Python3

# import sympy
from sympy import *

x = symbols('x')
expr = sin(x)**2 + cos(x)**2

print("Before Simplification : {}".format(expr))

# Use sympy.trigsimp() method
smpl = trigsimp(expr)

print("After Simplification : {}".format(smpl))

# This trigonometric expansion also be done using by simplify method

expr1 = sin(x)**2 + cos(x)**2

print("Using simplify method : {}" .format(simplify(expr1)))

Output:

Before Simplification : sin(x)**2 + cos(x)**2
After Simplification : 1
Using simplify method : 1

Example #2:

Python3

# import sympy
from sympy import *

x = symbols('x')
expr = sin(x)**4 - 2 * cos(x)**2 * sin(x)**2 + cos(x)**4

print("Before Simplification : {}".format(expr))

# Use sympy.trigsimp() method
smpl = trigsimp(expr)

print("After Simplification : {}".format(smpl))

# This trigonometric expansion also be done using by simplify method

expr1 = sin(x)**4 - 2 * cos(x)**2 * sin(x)**2 + cos(x)**4

print("Using simplify method : {}" .format(simplify(expr1)))

Output:

Before Simplification : sin(x)**4 - 2*cos(x)**2*sin(x)**2 + cos(x)**4
After Simplification : cos(4*x)/2 + 1/2
Using simplify method : cos(4*x)/2 + 1/2