4cos2a если sina = 1/4

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Given that sina = 1/4, we can find the value of cosa using the Pythagorean identity sin^2(a) + cos^2(a) = 1.

sin^2(a) + cos^2(a) = 1
(1/4)^2 + cos^2(a) = 1
1/16 + cos^2(a) = 1
cos^2(a) = 1 - 1/16
cos^2(a) = 15/16
cos(a) = ±√(15)/4

Now we can substitute the value of sina and cosa into the expression 4cos2a:

4cos2a = 4(2cos^2(a) - 1)
4cos2a = 4(2(15/16) - 1)
4cos2a = 4(30/16 - 1)
4cos2a = 4(15/8 - 8/8)
4cos2a = 4(7/8)
4cos2a = 7

Therefore, when sina = 1/4, 4cos2a = 7.