125. Prove the following identity :
sin A+cos A sin A-cos A
+
sin A-cos A sin A+cos A
2
2 sin? A-1
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Answer:
sinA+cosA+sinA+cosAsinA−cosA=(sinA−cosA)(sinA+cosA)(sinA+cosA)2+(sinA−cosA)(sinA+cosA)(sinA−cosA)2
=sin2A−cos2Asin2A+cos2A+2sinAcosA+sin2A+cos2A−2sinAcosA
=sin2A−cos2A2
=sin2A−(1−sin2A)2=2sin2A−12
=2(1−cos2A)−12=1−2cos2A2
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Answer:
sinA+cosA sin A - cosA + sinA - cosA sinA+ cosA
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