Q. 165.0( 2 Votes )

If cosA – sin A =

Answer :

Formula: - (i) a2 + b2 + 2ab = (a + b)2


cosA – sin A = √2 sin A


Squaring both sides we get,


(cos A – sin A)2 = 2 sin2A


cos2A + sin2A – 2cos A sin A = 2 sin2A


cos2 A – 2cos A sin A = sin2 A


Adding cos2 A both sides we get,


cos2A – 2cos A sinA + cos2A = sin2A + cos2A


2cos2 A = sin2 A + cos2 A + 2 cos A sin A


2cos2 A = (sinA + cosA)2


√2cosA = sinA + cosA


L.H.S = R.H.S


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