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OpenStudy (anonymous):
Prove (sinA-cosA)/sina + (cosA-sinA)/cosA=2-secAcscA
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OpenStudy (mathmath333):
\(\large\tt \begin{align} \color{black}{\dfrac{sinA-cosA}{sinA} + \dfrac{cosA-sinA}{cosA}\\~\\ =\dfrac{sinA}{sinA}-\dfrac{cosA}{sinA} + \dfrac{cosA}{cosA}-\dfrac{sinA}{cosA}\\~\\ =1-\dfrac{cosA}{sinA} + 1-\dfrac{sinA}{cosA}\\~\\ =2-\dfrac{cosA}{sinA}-\dfrac{sinA}{cosA}\\~\\ =2-(\dfrac{cosA}{sinA}+\dfrac{sinA}{cosA})\\~\\ =2-\dfrac{cos^2A+sin^2A}{sinAcosA}\\~\\ =2-\dfrac{1}{sinAcosA}\\~\\ =2-cosecAsecA\\~\\}\end{align}\)
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