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 sympyfrom sympy import *x = symbols('x')expr = sin(x)**2 + cos(x)**2print("Before Simplification : {}".format(expr)) # Use sympy.trigsimp() methodsmpl = trigsimp(expr) print("After Simplification : {}".format(smpl))# This trigonometric expansion also be done using by simplify methodexpr1 = sin(x)**2 + cos(x)**2print("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 sympyfrom sympy import *x = symbols('x')expr = sin(x)**4 - 2 * cos(x)**2 * sin(x)**2 + cos(x)**4print("Before Simplification : {}".format(expr)) # Use sympy.trigsimp() methodsmpl = trigsimp(expr) print("After Simplification : {}".format(smpl)) # This trigonometric expansion also be done using by simplify methodexpr1 = sin(x)**4 - 2 * cos(x)**2 * sin(x)**2 + cos(x)**4print("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
