Question

Sin²x + 5 sinxcosx + 4cos²x = 0 ​

Answer 1

Ответ: ответ на фото

Объяснение:

Answer 2

To solve the equation sin²x + 5sinxcosx + 4cos²x = 0, we can use trigonometric identities to simplify it.

First, we can rewrite the equation using the identity sin²x = 1 - cos²x:

(1 - cos²x) + 5sinxcosx + 4cos²x = 0

Expanding the equation:

1 - cos²x + 5sinxcosx + 4cos²x = 0

Rearranging the terms:

5sinxcosx - cos²x + 4cos²x + 1 = 0

Combining like terms:

(5sinx - 1)cos²x + 1 = 0

Now, we can solve this quadratic equation in terms of cosx:

(5sinx - 1)cos²x + 1 = 0

Since cos²x cannot be zero, we can divide the entire equation by cos²x:

(5sinx - 1) + 1/cos²x = 0

Simplifying further:

5sinx - 1 + 1/cos²x = 0

Now, we have a single equation involving sinx and cosx. We can use the identity sinx = sqrt(1 - cos²x) to substitute for sinx:

5(sqrt(1 - cos²x)) - 1 + 1/cos²x = 0

Simplifying:

5sqrt(1 - cos²x) + 1/cos²x - 1 = 0

Multiplying through by cos²x:

5cos²x(sqrt(1 - cos²x)) + 1 - cos²x = 0

Now, we have an equation only involving cosx. Let's substitute y = cosx to simplify the notation:

5y²(sqrt(1 - y²)) + 1 - y² = 0

This equation is a quadratic equation in terms of y. We can solve it by factoring or using the quadratic formula. Once we find the values of y, we can substitute them back to cosx and solve for x.