Question

What is formula of cos4x?

Answer 1

hey friend the formula of cos4x is.

= cos(2x)cos(2x) - sin(2x)sin(2x) = cos^2(2x) - sin^2(2x) = cos^2(2x) - (1 - cos^2(2x)) = 2cos^2(2x) - 1. cos(2x) = 2cos^2(x) - 1.

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Answer 2

To find:

cos 4x formula

Solution:

cos 4x = cos(2x+2x)

           = cos2x.cos2x - sin2x.sin2x     (   cos(a+b) =  cosa.cosb - sina.sinb   )

           = cos^2(2x) - sin^2(2x)

           = cos^2x - (1 - cos^2(2x))            (   sin^2(x) = 1 - cos^2(x)    )

           = 2cos^2(2x) - 1

           = 2cos^2(x+x) - 1

           = 2((cos^2(x) - sin^2(x))^2 - 1        (   cos(a+b) =  cosa.cosb - sina.sinb   )    

           = 2((2cos^2(x) - 1)^2 - 1                 (   sin^2(x) = 1 - cos^2(x)    )

           = 2[4cos^4(x) - 4cos^2(x) + 1] -1

           = 8(cos^4(x)) - 8(cos^2(x)) + 1

           = 8(cosx)^4 - 8(cosx)^2 + 1

Hence,  cos 4x =  8(cosx)^4 - 8(cosx)^2 + 1