Question

(Sin альфа +cos альфа)²

Answer 1

Пошаговое объяснение:

(sinα + cosα)² -2sinαcosα= разложим квадрат двучлена

sin²α+2sinαcosα+cos²α-2sinαcosα= взаимоуничтожим подобные

sin²α+cos²α= основное тригонометрич. тождество

Answer 2

To simplify the expression (sin α + cos α)², you can expand it using the binomial theorem or use trigonometric identities. I'll use trigonometric identities for this:

Recall the trigonometric identity:

(sin θ + cos θ)² = sin² θ + 2sin θ cos θ + cos² θ

In this case, θ is replaced with α:

(sin α + cos α)² = sin² α + 2sin α cos α + cos² α

Now, you can use the Pythagorean identity for sine and cosine:

sin² α + cos² α = 1

So, the expression simplifies to:

(sin α + cos α)² = 1 + 2sin α cos α

That's the simplified form of (sin α + cos α)².