The following Python code obtains the trigonometric identity of cos(3x) by using Euler's formula.: from sympy import Symbol, E, I, re,sin,cos x=Symbol('x',real=True) a=E**(I*x) b=a.expand(complex=True) print(b) c=a**3 d=c.expand(complex=True).expand(trig=True) print(d) print(re(d)) f=c.expand(complex=True) print(re(f)) print((re(f)-re(d)).expand(trig=True))   Homework: Adapt the previous Python code to show the trigonometric identity of sin(5x)

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The following Python code obtains the trigonometric identity of cos(3x) by using Euler's formula.:

from sympy import Symbol, E, I, re,sin,cos

x=Symbol('x',real=True)

a=E**(I*x)

b=a.expand(complex=True)

print(b)

c=a**3

d=c.expand(complex=True).expand(trig=True)

print(d)

print(re(d))

f=c.expand(complex=True)

print(re(f))

print((re(f)-re(d)).expand(trig=True))

 

Homework: Adapt the previous Python code to show the trigonometric identity of sin(5x)

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