Triqonometriyanın əsas düsturları

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Triqonometriyanın əsas düsturları:

 \cos^{2} A + \sin^{2} A = 1 \,
Failed to parse (lexing error): \cos (a+b)= \cos a \cdot \cos b – \sin a \cdot \sin b \,
\cos (a-b)= \cos a \cdot \cos b + \sin a \cdot \sin b \,
\sin (a+b)= \sin a \cdot \cos b + \cos a \cdot \sin b \,
Failed to parse (lexing error): \sin (a-b)= \sin a \cdot \cos b – \cos a \cdot \sin b \,


\tan(a+b) = \frac{\tan a + tan b}{1- \tan a\cdot \tan b}\  \,


Failed to parse (lexing error): \tan (a-b) = \frac{\tan a – \tan b}{1+ \tan a\cdot \tan b}\ \,


Failed to parse (lexing error): \cos 2a= \cos^2 a – \sin^2 a=2 \cos^2 a -1= 1 – 2 \sin^2 a \,


\sin 2a=2 \sin a\cdot \cos a  \,


\cos^2 a=\frac{1}{2}\ (1+ \cos 2a) \,
\sin^2 a=\frac{1}{2}\ (1- \cos 2a) \,
\cos a \cdot \cos b =\frac{1}{2}( \cos (a+b)+ \cos (a-b))
\sin a \cdot \sin b =\frac{1}{2}( \cos (a-b)- \cos (a+b))
\sin a \cdot \cos b =\frac{1}{2}( \sin (a+b)+ \sin (a-b))


\cos a + \cos b=2 \cos\frac{ a+b }{ 2 }\cdot \cos\frac{ a-b }{2}\ \,
Failed to parse (lexing error): \cos a – \cos b=-2 \sin\frac{ a+b }{ 2 }\cdot \sin\frac{ a-b }{2}\ \,
\sin a + \sin b=2 \sin \frac{ a+b }{ 2 }\cdot \cos\frac{ a-b }{2}\ \,
Failed to parse (lexing error): \sin a – \sin b=2 \cos \frac{ a+b }{ 2 }\cdot \sin\frac{ a-b }{2}\ \,



\tan \frac{A}{2} =t isə, onda: Elədə

\sin\ A = {{2\,t} \over {1+t^{2}}}
\cos\ A = {{1-t^{2}} \over {1+t^{2}}}
\tan\ A = {{2\,t}\over {1-t^{2}}}

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