CBSE Class 11-science Answered
IF CosX+SinX=?2.CosX
P.T CosX-SinX=?2.SinX
Asked by chethan U | 22 Jul, 2012, 05:33: PM
Expert Answer
Answer : Given : cosA+ sinA = (underroot2 )*cosA
To prove : cosA - sinA = (underroot2 )*sinA
we have ,
=> (cosA+sinA)2 + (cosA -sinA) = 2
=> ( (underroot 2 ) *(cosA) ) + (cosA-sinA)2 = 2 { using given equation}
=> 2cos2A + (cosA-sinA)2 = 2
=> (cosA-sinA)2 = 2 - 2cos2A
=> (cosA - sinA)2 = 2 ( sin2A ) { using 1 - cos2A = sin2A }
taking the square root both the sides we get ,
=> cosA- sinA = (underroot2 )*sinA
Hence Proved
Answered by | 22 Jul, 2012, 07:41: PM
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