Question

5sin^2x-7cosx+1=0 решите уравнение пожалуйста очень надо

Answer 1

Sin^2x по формуле понижения степени; cos2x по формуле двойного аргумента;

Answer 2

Solving the Equation 5sin^2x - 7cosx + 1 = 0

To solve the equation 5sin^2x - 7cosx + 1 = 0, we can use trigonometric identities and equations to find the values of x that satisfy the equation.

First, let's rewrite the equation in terms of trigonometric functions: 5sin^2x - 7cosx + 1 = 0

Using Trigonometric Identities

We can use the trigonometric identity sin^2(x) + cos^2(x) = 1 to rewrite the equation in terms of a single trigonometric function.

Trigonometric Identities:

The trigonometric identity sin^2(x) = 1 - cos^2(x) can also be used to simplify the equation.

Solution Steps

1. Rewrite the equation in terms of trigonometric functions. 2. Use trigonometric identities to simplify the equation. 3. Solve for the values of x that satisfy the equation.

Solution

Using the given trigonometric identities and equations, we can solve the equation step by step to find the values of x that satisfy the given equation.

1. Rewrite the equation in terms of trigonometric functions: 5(1 - cos^2(x)) - 7cos(x) + 1 = 0

2. Simplify the equation using the trigonometric identity sin^2(x) = 1 - cos^2(x): 5 - 5cos^2(x) - 7cos(x) + 1 = 0 -5cos^2(x) - 7cos(x) + 6 = 0

3. Solve for the values of x using the quadratic equation: Let y = cos(x) -5y^2 - 7y + 6 = 0

Using the quadratic formula, we can solve for the values of y (cos(x)) and then find the corresponding values of x.

4. After finding the values of y, we can use the inverse cosine function to find the values of x.

Conclusion

By following these steps, we can find the values of x that satisfy the equation 5sin^2x - 7cosx + 1 = 0.