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

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Anonymous Anonymous

24-07-2014
Mathematics

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

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luana luana · Answer 1 · 2014-07-24T16:38:36-04:00

\(\frac{cosA}{ \frac{cosA}{cosA}- \frac{sinA}{cosA}}+ \frac{sinA}{ \frac{sinA}{sinA}- \frac{cosA}{sinA} }=sinA+cosA\\ \frac{cosA}{ \frac{cosA-sinA}{cosA}+ \frac{sinA}{ \frac{sinA-cosA}{sinA} } }=sinA+cosA\\ \frac{ cos^{2}A }{cosA-sinA} }- \frac{sin^{2}A }{cosA-sinA}=sinA+cosA\\ \frac{ cos^{2}A-sin^{2}A }{cosA-sinA}=sinA+cosA\\cos(2A)=(sinA+cosA)(cosA-sinA)\\ cos(2A)=(sinA+cosA)(sinA-cosA)\\cos(2A)=sin^{2}A - cos^{2}A\\cos2A=cos2A \\1=1\)