Trig Identities -- Sage

#1)Pythagorean Trig Identities f(x)=sin(x)^2+cos(x)^2 show(f(x)) show(f(x).simplify_trig()) g(x)=f(x)/cos(x)^2 show(g(x)) show(g(x).simplify_trig()) h(x)=f(x)/sin(x)^2 show(h(x)) show(h(x).simplify_trig())

 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x\right)^{2} + \sin\left(x\right)^{2}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}1$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{\cos\left(x\right)^{2} + \sin\left(x\right)^{2}}{\cos\left(x\right)^{2}}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{\cos\left(x\right)^{2}}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{\cos\left(x\right)^{2} + \sin\left(x\right)^{2}}{\sin\left(x\right)^{2}}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{\sin\left(x\right)^{2}}$

#2)Sum and Diff of 2 Angles Trig Identities var('y') f(x)=sin(x+y) show(f(x)) show(f(x).simplify_trig()) f(x)=sin(x-y) show(f(x)) show(f(x).simplify_trig()) f(x)=cos(x+y) show(f(x)) show(f(x).simplify_trig()) f(x)=cos(x-y) show(f(x)) show(f(x).simplify_trig())

 $\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(x + y\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(y\right) \sin\left(x\right) + \cos\left(x\right) \sin\left(y\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(x - y\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(y\right) \sin\left(x\right) - \cos\left(x\right) \sin\left(y\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x + y\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x\right) \cos\left(y\right) - \sin\left(x\right) \sin\left(y\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x - y\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x\right) \cos\left(y\right) + \sin\left(x\right) \sin\left(y\right)$

#3)Double Angle Trig Identities f(x)=(1+cos(2*x))/2 show(f(x)) show(f(x).simplify_trig()) f(x)=(1-cos(2*x))/2 show(f(x)) show(f(x).simplify_trig())

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, \cos\left(2 \, x\right) + \frac{1}{2}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x\right)^{2}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{2} \, \cos\left(2 \, x\right) + \frac{1}{2}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(x\right)^{2}$

Trig Identities

2405 days ago by MATH4R2013