Question

Sinx+1.5ctgx=0 пжжжжжжжжжжжжжжжжжжжжжжж

Answer 1

Ответ:[x=2π/3+2πn

[x=4π/3+2πn, n принадлежит Z

Пошаговое объяснение:

sinx+1,5(cosx/sinx)=0

(sinx^2+1,5cosx)/sinx=0

ОДЗ: sinx≠0; x≠πn, n(принадлежит)Z

sinx+3cosx/2sinx=0

(2sinx^2+3cosx)/2sinx=0

2(1-cosx^2)+3cosx=0

2cosx^2-3cosx-2=0

Замена переменных:cosx=t

2t^2-3t-2=0

D=9-8=1

[t=2;

[t=-0,5

Переход к исходным переменным:

[cosx=2;

[cosx=-0,5

[Нет корней;

[x=±arccos(-0,5)+2πn, n принадлежит Z

Развернутый вид второго корня*:

[x=2π/3+2πn

[x=4π/3+2πn, n принадлежит Z

Answer 2

To solve the equation $\sin(x) + 1.5 \cot(x) = 0$, we first need to rewrite the cotangent in terms of sine and cosine.

Recall that $\cot(x) = \frac{1}{\tan(x)}$, and $\tan(x) = \frac{\sin(x)}{\cos(x)}$.

So, we have $\cot(x) = \frac{1}{\frac{\sin(x)}{\cos(x)}} = \frac{\cos(x)}{\sin(x)}$.

Now the equation becomes $\sin(x) + 1.5 \cdot \frac{\cos(x)}{\sin(x)} = 0$.

To solve this equation, we can find a common denominator, which is $\sin(x)$:

$\sin^2(x) + 1.5\cos(x) = 0$.

Now, to further simplify this equation, we can use the trigonometric identity $\sin^2(x) + \cos^2(x) = 1$ to replace $\sin^2(x)$ with $1 - \cos^2(x)$:

$1 - \cos^2(x) + 1.5\cos(x) = 0$.

This is now a quadratic equation in terms of $\cos(x)$. We can solve for $\cos(x)$ by rearranging the terms:

$\cos^2(x) - 1.5\cos(x) - 1 = 0$.

Now, we can solve this quadratic equation for $\cos(x)$. Once we find the values of $\cos(x)$, we can find the corresponding values of $x$ by taking the inverse cosine.

Keep in mind that there may be multiple solutions for $x$, so it's always a good practice to check your answers in the original equation to ensure they satisfy it.