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Dvinal [7]
4 years ago
14

Cos A/1-tan A + sin A/1-cot A =sin A + cos A

Mathematics
1 answer:
Vadim26 [7]4 years ago
5 0
\frac{cosA}{ \frac{cosA}{cosA}- \frac{sinA}{cosA}}+ \frac{sinA}{ \frac{sinA}{sinA}- \frac{cosA}{sinA}  }=sinA+cosA\\  \frac{cosA}{ \frac{cosA-sinA}{cosA}+ \frac{sinA}{ \frac{sinA-cosA}{sinA} }  }=sinA+cosA\\ \frac{ cos^{2}A }{cosA-sinA} }- \frac{sin^{2}A }{cosA-sinA}=sinA+cosA\\
 \frac{ cos^{2}A-sin^{2}A }{cosA-sinA}=sinA+cosA\\cos(2A)=(sinA+cosA)(cosA-sinA)\\
cos(2A)=(sinA+cosA)(sinA-cosA)\\cos(2A)=sin^{2}A - cos^{2}A\\cos2A=cos2A  \\1=1
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