Tg2x=0,5
2x=arctg0,5+πn
x=1/2*arctg0,5+ππn/2,n∈z
tg2x=2
2x=arctg02+πn
x=1/2*arctg2+ππn/2,n∈z
46^2-26^2=46x46-26x26=2116-676=1440
35^2-25^2=35x35-25x25=1225-625=600
Решение задания смотри на фотографии
Tg⁴x + ctg⁴x + tg²x + ctg²x = 4
Обозначим tg²x + ctg²x = a, тогда a² = tg⁴x + ctg⁴x + 2⇒ tg⁴x + ctg⁴x = a² -2
a<span>² -2 + a - 4 = 0
</span>a² + a - 6 = 0
a = -3 не подходит, т.к. а - сумма квадратов
a = 2
<span> tg²x + ctg²x = 2
</span>Обозначим tgx + ctgx = t, тогда t² = tg²x + ctg²x + 2⇒ <span>tg²x + ctg²x </span> = t² -2
t<span>² -2 - 2 = 0
t</span>² - 4 = 0<span>
</span>(t - 2)(t + 2) = 0
t = 2
t = -2
<span> tgx + ctgx = 2
</span>sinx/cosx + cosx/sinx = 2
(sin²x + cos²x) / (sinx·cosx) = 2
1 / <span>(sinx·cosx) = 2
</span><span>sinx·cosx = 1/2
</span>1/2 sin2x = 1/2
sin2x = 1
2x = π/2 + 2πn
x = π/4 + πn
<span>tgx + ctgx = -2
</span>sinx/cosx + cosx/sinx = -2
(sin²x + cos²x) / (sinx·cosx) = -2
1 / <span>(sinx·cosx) = -2
</span><span>sinx·cosx = -1/2
</span>1/2 sin2x = -1/2
sin2x = -1
2x = -π/2 + 2πn
<span>x = -π/4 + πn
</span>Ответ: <span>x = π/4 + πm/2</span>