how is cos square x =1+cos2x/2

Asked by AADESH CHARAN | 28th Apr, 2013, 07:55: PM

Expert Answer:

This is a property 
 
It can be proved by using the cos(A+B) = cosAcosB - sinAsinB
 
(1+cos2x)/2 = (1+cos(x+x))/2 = (1+(cosx)^2 - (sinx)^2)/2
 
Now 1-(sinx)^2 = (cosx)^2
 
Hence,  (1+(cosx)^2 - (sinx)^2)/2 = ((cosx)^2 + (cosx)^2)/2 = (cosx)^2 = LHS
 
Hence proved

Answered by  | 29th Apr, 2013, 02:13: AM

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