Question

Sin²x+2cos²x=1 vvvvvvvvvvvvvvvvvvvvvvvvvvvvv

Answer 1

Записываем в виде
(sin²α + cos²α) + cos²α = 1
cos²α = 0
cosα = π*n - ОТВЕТ

Answer 2

It looks like you've provided a trigonometric identity:

$\sin^2(x) + 2\cos^2(x) = 1$

This is known as the Pythagorean trigonometric identity, which holds true for any angle $x$ in a right triangle. It's derived from the Pythagorean theorem. In a right triangle, if you have an angle $x$ and the adjacent side is $a$ and the hypotenuse is $h$, then you have:

$\sin(x) = \frac{a}{h}$ $\cos(x) = \frac{\sqrt{h^2 - a^2}}{h}$

Substitute these values into the identity:

$\sin^2(x) + 2\cos^2(x) = \left(\frac{a}{h}\right)^2 + 2\left(\frac{\sqrt{h^2 - a^2}}{h}\right)^2$

Simplify:

$\frac{a^2}{h^2} + 2\frac{h^2 - a^2}{h^2} = \frac{a^2 + 2h^2 - 2a^2}{h^2} = \frac{h^2}{h^2} = 1$

So, the identity is verified. It's a fundamental relationship between the sine and cosine functions in trigonometry.