tan^2(x) + 1 = sec^2(x)
Given sin(x) = 1/4, we can find cos(x) using the Pythagorean identity: sin^2(x) + cos^2(x) = (1/4)^2 + cos^2(x) = 1/16 + cos^2(x) = cos^2(x) = 1 - 1/1cos^2(x) = 15/1cos(x) = ±√(15)/4
Now that we have sin(x) and cos(x), we can find tan(x)tan(x) = sin(x) / cos(xtan(x) = (1/4) / (±√(15)/4tan(x) = 1/√(15) or -1/√(15)
Therefore, tg(x) = 1/√(15) or -1/√(15)
tan^2(x) + 1 = sec^2(x)
Given sin(x) = 1/4, we can find cos(x) using the Pythagorean identity: sin^2(x) + cos^2(x) =
(1/4)^2 + cos^2(x) =
1/16 + cos^2(x) =
cos^2(x) = 1 - 1/1
cos^2(x) = 15/1
cos(x) = ±√(15)/4
Now that we have sin(x) and cos(x), we can find tan(x)
tan(x) = sin(x) / cos(x
tan(x) = (1/4) / (±√(15)/4
tan(x) = 1/√(15) or -1/√(15)
Therefore, tg(x) = 1/√(15) or -1/√(15)