Question

Tg(arctg2-arctg1/2) a)3/4 b)3/2 c)4/3 d)2/3

Answer 1

$\tan(\arctan2-\arctan\frac{1}{2})=\\=\frac{\tan(\arctan2)-\tan(\arctan\frac{1}{2})}{1+\tan(\arctan2)\tan(\arctan\frac{1}{2})}=\frac{2-0.5}{2}=1.5/2=0.75=3/4$

Вариант А

Answer 2

To simplify the expression tg(arctg2 - arctg(1/2)), we can use the trigonometric identity:

tg(a - b) = (tg(a) - tg(b)) / (1 + tg(a) * tg(b))

Let's substitute a = arctg(2) and b = arctg(1/2):

tg(arctg(2) - arctg(1/2)) = (tg(arctg(2)) - tg(arctg(1/2))) / (1 + tg(arctg(2)) * tg(arctg(1/2)))

Now, let's simplify tg(arctg(2)) and tg(arctg(1/2)):

tg(arctg(2)) = 2 tg(arctg(1/2)) = 1/2

Substituting these values back into the expression:

tg(arctg(2) - arctg(1/2)) = (2 - 1/2) / (1 + 2 * 1/2) = (3/2) / (3/2) = 1

Therefore, the simplified expression is 1. None of the given options (a), b), c), d)) match the simplified expression of 1.