Question

5/1-sin^2(x) + 7/cos(x) = 6 (13 задание егэ)

Answer 1

Ответ: Недавно решал такое

a)+-2pi/3+2pi n

б) -2pi/3; -4pi/3

как-то так получилось

Пошаговое объяснение:

(в фото)

Answer 2

To solve the equation $\frac{5}{1-\sin^2(x)} + \frac{7}{\cos(x)} = 6$, you can follow these steps:

1. Simplify the equation: Rewrite $\frac{5}{1-\sin^2(x)}$ using the trigonometric identity $\sin^2(x) + \cos^2(x) = 1$. This will help simplify the expression.

   $\frac{5}{\cos^2(x)} + \frac{7}{\cos(x)} = 6$

2. Combine fractions: Find a common denominator and combine the fractions on the left side of the equation.

   $\frac{5}{\cos^2(x)} + \frac{7}{\cos(x)} - 6 = 0$

3. Multiply by the common denominator: Multiply each term by the common denominator ($\cos^2(x)$) to eliminate fractions.

   $5 + 7\cos(x) - 6\cos^2(x) = 0$

4. Rearrange the equation: Move all terms to one side of the equation to set it equal to zero.

   $6\cos^2(x) - 7\cos(x) - 5 = 0$

5. Factor or use the quadratic formula: Factor the quadratic expression or use the quadratic formula to find the values of $\cos(x)$.

   The quadratic formula is given by $\cos(x) = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$, where $a = 6$, $b = -7$, and $c = -5$.

   $\cos(x) = \frac{7 \pm \sqrt{(-7)^2 - 4(6)(-5)}}{2(6)}$

   Simplify the expression to find the values of $\cos(x)$.

6. Use the inverse cosine function: Once you have the values of $\cos(x)$, use the inverse cosine function to find the corresponding values of $x$.

   $x = \cos^{-1}(\text{value})$

Remember to check if the solutions are within the appropriate domain, typically $0 \leq x \leq 2\pi$ or $-\pi \leq x \leq \pi$, depending on the context of the problem.