Question

Решите уравнение 1-cos x/2 =tg x/4

Answer 1

$1 - cos\frac{x}{2} = 2sin^{2}\frac{x}{4}$
$2sin^{2}\frac{x}{4} = \frac{sin\frac{x}{4}}{cos\frac{x}{4}}$
$2sin\frac{x}{4} * cos\frac{x}{4} = 1$
$sin\frac{x}{2} = 1$
$arcsin(1) = \frac{x}{2}$
$\frac{\pi}{2} = \frac{x}{2}$
$x = \pi$

Answer 2

1-cosx/2=2sin^2(x/4), 2sin^2(x/4)=(sinx/4)/(cosx/4) 2sin^2(x/4)*cosx/4-sinx/4=0, cosx/4 ≠ 0. sinx/4 вынесем за скобки . 1) sinx/4=0, x/4=Пn, x=4Пn. 2) 2sinx/4*cosx/4-1=0, sinx/2=1, x/2=П/2+2Пn, x= П+4Пn Ответ П+4Пn, 4Пn
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