Question

Sin^2x+2sinxcosx-3cos^2x=0

Answer 1

Sin^2x+2sinxcosx-3cos^2x=0

Используем переместительный закон, чтобы изменить порядок членов

Sn^2xi+2sin(x)cos(x)-3c

Упрощаем выражение, используя 2*sin(t)*cos(t)=sin(2*t)

Получаем ответ: Sn^2xi+sin(2x)-3c

Answer 2

The equation you've provided is a trigonometric equation involving the sine and cosine functions. It's a quadratic equation in terms of these trigonometric functions. Let's solve it step by step:

Given equation: sin^2(x) + 2sin(x)cos(x) - 3cos^2(x) = 0

First, we can use the trigonometric identity sin^2(x) + cos^2(x) = 1 to replace sin^2(x) in the equation:

1 - cos^2(x) + 2sin(x)cos(x) - 3cos^2(x) = 0

Now, let's focus on the terms involving cos^2(x) and sin(x)cos(x):

-4cos^2(x) + 2sin(x)cos(x) + 1 = 0

Divide the entire equation by -1 to simplify the coefficients:

4cos^2(x) - 2sin(x)cos(x) - 1 = 0

Now, let's factor out a common term:

2cos(x)(2cos(x) - sin(x)) - 1 = 0

So, we have a factorized form of the equation:

2cos(x)(2cos(x) - sin(x)) - 1 = 0

Now, you can solve this equation by considering the values of cos(x) and sin(x) that satisfy it. This equation will have multiple solutions for x. If you need the specific solutions, you might need to use numerical methods or a calculator to find the approximate values.