Вычислите sin2a, cos2a и tg2a, если cosa=3/5 и 0

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Given that cos(a) = 3/5, we can find sin(a) using the Pythagorean identity sin^(2)(a) + cos^(2)(a) = 1 as follows:

sin^(2)(a) = 1 - cos^(2)(a)
sin^(2)(a) = 1 - (3/5)^(2)
sin^(2)(a) = 1 - 9/25
sin^(2)(a) = 25/25 - 9/25
sin^(2)(a) = 16/25
sin(a) = √(16/25) = 4/5

Now, let's calculate the trigonometric functions for 2a:

sin(2a) = 2 sin(a) cos(a)
sin(2a) = 2 (4/5) (3/5)
sin(2a) = 24/25

cos(2a) = cos^(2)(a) - sin^(2)(a)
cos(2a) = (3/5)^(2) - (4/5)^(2)
cos(2a) = 9/25 - 16/25
cos(2a) = -7/25

tan(2a) = sin(2a) / cos(2a)
tan(2a) = (24/25) / (-7/25)
tan(2a) = -24/7

Therefore, the values are:

sin(2a) = 24/25
cos(2a) = -7/25
tan(2a) = -24/7