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Answer»

ong>Step-by-step EXPLANATION:

\frac{sinA + cosA}{sinA - cosA} × \frac{sinA - cosA}{sinA + cosA}

=\frac{(sinA + cosA)^{2} + (sinA - cosA)^{2} }{(sinA + cosA)(sinA -cosA)}

=\frac{sin^{2}A +2sinAcosA +cos^{2}A + sin^{2}A -2sinAcosA +cos^{2}A}{sin^{2} A- cos^{2}A }

=\frac{2(sin^{2}A + cos^{2}A)}{sin^{2}A - cos^{2}A }

=\frac{2(1)}{sin^{2}A - cos^{2}A }

=\frac{2}{sin^{2}A - cos^{2}A }   (FIRST ANSWER)

=\frac{2}{sin^{2}A + 1 - cos^{2}A -1 }                                                  

=\frac{2}{sin^{2}A + sin^{2}A -1 }

=\frac{2}{2sin^{2}A -1 } (second answer)

from the first answer,

\frac{2}{sin^{2}A - cos^{2}A }  

=\frac{2}{1 - cos^{2}A - cos^{2}A }

=\frac{2}{1 - 2cos^{2}A }(third answer)    


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