Question
Sun July 22, 2012 By: Chethan U

IF CosX=SinX=[squareroot]?2.SinX P T CosX-SinX=[squareroot]?2.SinX

Expert Reply
Sun July 22, 2012
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  { using given equation}
=> 2cos2 X+ (cosX-sinX)= 2  
=> (cos- sinX)= 2 - 2cos2 X
=> (cosX - sinX)= 2 ( sin2X )    { using 1 - cos2 X = sin2A }
 
taking the square root both the sides we get ,
 
=>  cos-  sinX = (underroot2 )*sinX
            Hence Proved 
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