Question
Sun July 22, 2012 By: Chethan U
How to prove this equation sir

IF CosX+SinX=?2.CosX P.T CosX-SinX=?2.SinX

Expert Reply
Sun July 22, 2012
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  { using given equation}
=> 2cos2A + (cosA-sinA)2 = 2  
=> (cosA-sinA)= 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 
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