Question

Задание на тест, заранее спасибо.

Answer 1

1)
$6 {sin}^{2} x - 4sin2x = - 1 \\ 6 {sin}^{2} x - 8sincosx + 1 = 0 \\ 6 {sin}^{2} x - 8sinxcosx + {sin}^{2} x + {cos}^{2} x = 0 \\ 7 {sin}^{2} x - 8sinxcosx + {cos}^{2} x = 0$
Разделим теперь всё на cos^2 (x),
cosx не равно 0
x не равно 2pi*n
$7 {tg}^{2} x - 8tgx + 1 = 0$
tgx = t
$7 {t}^{2} - 8t + 1 = 0$
D = 64 - 4*7 = 36
t1 = (8 + 6)/2*7 = 1
t2 = (8 - 6)/2*7 = 1/7
1) tgx = 1
x = arctg1 + pi*n
x = pi/4 + pi*n, n € Z.
2) tgx = 1/7
x = arctg1/7 + pi*n, n € Z.
Ответ: А)

2) f(x) = (6x + 1)*(6x - 1) = 36x^2 - 1
f'(x) = 36*2*x - 0 = 72x
f'(0,5) = 72*0,5 = 36
f'(-1) = 72*(-1) = -72
Ответ: Е)

3)
$log_{5}( \frac{625 {c}^{2}d }{0.04 {a}^{3}b } ) = log_{5}(625 {c}^{2}d ) - log_{5}(0.04 {a}^{3}b ) = log_{5}(625) + log_{5}( {c}^{2} ) + log_{5}(d) - (log_{5}(0.04) + log_{5}( {a}^{3} ) + log_{5}(b)) = 4 + 2 log_{5}(c) + log_{5}(d) - ( - 2) - 3 log_{5}( a ) - log_{5}(b) = 6 + 2 log_{5}(c) + log_{5}(d) - 3 log_{5}(a) - log_{5}(b)$
Ответ: E)