Question

Cos^2 x=2sin⁡x-sin^2 x

Answer 1

Ответ:

Пошаговое объяснение:

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Answer 2

To solve the trigonometric equation $\cos^2 x = 2\sin x - \sin^2 x$, we can use trigonometric identities to simplify and solve for $x$. Here's how to do it step by step:

Starting with the given equation: $\cos^2 x = 2\sin x - \sin^2 x$

Let's use the Pythagorean identity $\sin^2 x + \cos^2 x = 1$ to replace $\cos^2 x$ in the equation: $1 - \sin^2 x = 2\sin x - \sin^2 x$

Simplify by canceling out the common $-\sin^2 x$ terms: $1 = 2\sin x$

Now, isolate $\sin x$ by dividing both sides by 2: $\sin x = \frac{1}{2}$

Now, to find the solutions for $x$, we need to determine the angles where the sine function equals $\frac{1}{2}$. These angles can be found in the unit circle or using trigonometric values:

In the unit circle, $\sin x = \frac{1}{2}$ at two angles: $x = \frac{\pi}{6} + 2\pi n$ and $x = \frac{5\pi}{6} + 2\pi n$, where $n$ is an integer.

So, the solutions for $x$ are: $x = \frac{\pi}{6} + 2\pi n$ and $x = \frac{5\pi}{6} + 2\pi n$, where $n$ is an integer.

These are the values of $x$ that satisfy the given equation.