Question

Срочно!!!Решите тригонометрические уравнения 1)cos4x+sin8x=0;2)5sin7x/2=8sin²7x/2

Answer 1

Вот. Если правильно прочла 2 пример то так

Answer 2

1) Cos4x + Sin8x = 0
Cos4x + 2Sin4xCos4x =0
Cos4x(1 + 2Sin4x) = 0
или Сos4x = 0                                                        или 1 + 2Sin4x = 0
       4x = $\frac{ \pi }{2} + \pi n,$n∈z           Sin4x = - 1/2
       $x = \frac{ \pi }{8} + \frac{ \pi n}{4} ,$n∈z     $4x = (- 1) ^{n+1} \frac{ \pi }{6} + \pi n,$n∈z
$x = (-1) ^{n+1} \frac{ \pi }{24} + \frac{ \pi n}{4}$ ,n∈z
2) $5Sin \frac{7x}{2} = 8Sin ^{2} \frac{7x}{2}$
$5Sin \frac{7x}{2} - 8Sin ^{2} \frac{7x}{2} = 0$
$Sin \frac{7x}{2} (5 - 8Sin \frac{7x}{2}) = 0$
$Sin \frac{7x}{2} = 0$                   $5 - 8Sin \frac{7x}{2} = 0$
$\frac{7x}{2} = \pi n, n∈z$           $Sin \frac{7x}{2} = \frac{5}{8}$
$x = \frac{2 \pi n}{7} , n∈z$        $x = (-1) ^{n} arcSin \frac{5}{8} + \pi n,n∈z$