| $$ Formules\ de\ trigonomètrie$$ |
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$$\sin^{2} \left( \alpha \right) +\cos^{2} \left( \alpha \right)
=1$$ $$ \cos^{2} \left( \alpha \right) =\frac{1}{1+\tan^{2} \left(
\alpha \right) } $$ $$ \tan \left( \alpha \right) =\frac{\sin
\left( \alpha \right) }{\cos \left( \alpha \right) } $$ $$
\sin^{2} \left( \alpha \right) =\frac{\tan^{2} \left( \alpha
\right) }{1+\tan^{2} \left( \alpha \right) } $$ $$1+\tan^{2}
\left( \alpha \right) =\frac{1}{\cos^{2} \left( \alpha \right) }
$$
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$$\sin \left( -x\right) =-\sin \left( x\right) $$ $$\cos \left(
-x\right) =\cos \left( x\right) $$ $$\tan \left( -x\right) =-\tan
\left( x\right) $$ $$\sin \left( \pi -x\right) =\sin \left(
x\right) $$ $$\cos \left( \pi -x\right) =-\cos \left( x\right) $$
$$\tan \left( \pi -x\right) =-\tan \left( x\right) $$ $$\sin
\left( \pi +x\right) =-\sin \left( x\right) $$ $$\cos \left( \pi
+x\right) =-\cos \left( x\right) $$ $$\tan \left( \pi +x\right)
=\tan \left( x\right) $$
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$$\sin \left( \frac{\pi }{2} -x\right) =\cos \left( x\right) $$
$$\cos \left( \frac{\pi }{2} -x\right) =\sin \left( x\right) $$
$$\tan \left( \frac{\pi }{2} -x\right) =\cot \left( x\right) $$
$$\sin \left( \frac{\pi }{2} +x\right) =\cos \left( x\right) $$
$$\cos \left( \frac{\pi }{2} +x\right) =-\sin \left( x\right) $$
$$\tan \left( \frac{\pi }{2} +x\right) =-\cot \left( x\right) $$
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$$ \sin \left( x+y\right) =\sin \left( x\right) \cos \left(
y\right) +\cos \left( x\right) \sin \left( y\right) $$ $$\sin
\left( x-y\right) =\sin \left( x\right) \cos \left( y\right) -\cos
\left( x\right) \sin \left( y\right) $$ $$ \cos \left( x+y\right)
=\cos \left( x\right) \cos \left( y\right) -\sin \left( x\right)
\sin \left( y\right) $$ $$\cos \left( x-y\right) =\cos \left(
x\right) \cos \left( y\right) +\sin \left( x\right) \sin \left(
y\right) $$ $$\tan \left( x+y\right) =\frac{\tan \left( x\right)
+\tan \left( y\right) }{1-\tan \left( x\right) \tan \left(
y\right) } $$ $$\tan \left( x-y\right) =\frac{\tan \left( x\right)
-\tan \left( y\right) }{1+\tan \left( x\right) \tan \left(
y\right) } $$
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$$\sin \left( 2x\right) =2\cdot \sin \left( x\right) \cdot \cos
\left( x\right) $$ $$\cos \left( 2x\right) =\cos^{2} \left(
x\right) -\sin^{2} \left( x\right) $$ $$2\cos^{2} \left( x\right)
=1+\cos^{2} \left( 2x\right) $$ $$2\sin^{2} \left( x\right)
=1-\cos^{2} \left( 2x\right) $$
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$$\sin \left( 2x\right) =\frac{2\tan \left( x\right) }{1+\tan^{2}
\left( x\right) } $$ $$\cos \left( 2x\right) =\frac{1-\tan^{2}
\left( x\right) }{1+\tan^{2} \left( x\right) } $$ $$\tan \left(
2x\right) =\frac{2\tan \left( x\right) }{1-\tan^{2} \left(
x\right) } $$
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$$\sin \left( 3x\right) =3\sin \left( x\right) -4\sin^{3} \left(
x\right) $$ $$\cos \left( 3x\right) =-3\cos \left( x\right)
+4\cos^{3} \left( x\right) $$
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$$\sin \left( x\right) +\sin \left( y\right) =2\sin \left(
\frac{x+y}{2} \right) \cos \left( \frac{x-y}{2} \right) $$ $$\sin
\left( x\right) -\sin \left( y\right) =2\sin \left( \frac{x-y}{2}
\right) \cos \left( \frac{x+y}{2} \right) $$ $$\cos \left(
x\right) +\cos \left( y\right) =2\cos \left( \frac{x+y}{2} \right)
\cos \left( \frac{x-y}{2} \right) $$ $$\cos \left( x\right) -\cos
\left( y\right) =-2\sin \left( \frac{x+y}{2} \right) \sin \left(
\frac{x-y}{2} \right) $$ $$\tan \left( x\right) +\tan \left(
y\right) =\frac{\sin \left( x+y\right) }{\cos \left( x\right) \cos
\left( y\right) } $$ $$\tan \left( x\right) -\tan \left( y\right)
=\frac{\sin \left( x-y\right) }{\cos \left( x\right) \cos \left(
y\right) } $$
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$$\sin \left( x\right) \cos \left( y\right) =\frac{1}{2} \left[
\sin \left( x+y\right) +\sin \left( x-y\right) \right] $$ $$\cos
\left( x\right) \cos \left( y\right) =\frac{1}{2} \left[ \cos
\left( x+y\right) +\cos \left( x-y\right) \right] $$ $$\sin \left(
x\right) \sin \left( y\right) =\frac{1}{2} \left[ \cos \left(
x-y\right) -\cos \left( x+y\right) \right] $$
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