CBSE Class 11-science Answered
IF CosX=SinX=[squareroot]?2.SinX
P T CosX-SinX=[squareroot]?2.SinX
Asked by chethan U | 22 Jul, 2012, 07:03: PM
Expert Answer
Answer : Given : cosX+ sinX = (underroot2 )*cosX
To prove : cosX - sinX = (underroot2 )*sinX
we have ,
=> (cosX+sinX)2 + (cosX -sinX) = 2
=> ( (underroot 2 ) *(cosX) ) + (cosX-sinX)2 = 2 { using given equation}
=> 2cos2 X+ (cosX-sinX)2 = 2
=> (cosX - sinX)2 = 2 - 2cos2 X
=> (cosX - sinX)2 = 2 ( sin2X ) { using 1 - cos2 X = sin2A }
taking the square root both the sides we get ,
=> cosX - sinX = (underroot2 )*sinX
Hence Proved
Answered by | 22 Jul, 2012, 08:54: PM
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