Question

(sin альфа + cos альфа)^2 + 1 - sin 2 альфа

Answer 1

Ответ: решение смотри на фотографии

Пошаговое объяснение:

Answer 2

To simplify the expression (sin α + cos α)^2 + 1 - sin 2α, let's break it down step by step:

Step 1: Expand the square of the binomial (sin α + cos α)^2. (sin α + cos α)^2 = sin^2 α + 2sin α cos α + cos^2 α

Step 2: Simplify the expression. (sin α + cos α)^2 + 1 - sin 2α = (sin^2 α + 2sin α cos α + cos^2 α) + 1 - sin 2α

Step 3: Use trigonometric identities. Recall the Pythagorean identity: sin^2 α + cos^2 α = 1

(sin^2 α + 2sin α cos α + cos^2 α) + 1 - sin 2α = (1 + 2sin α cos α) + 1 - sin 2α

Step 4: Combine like terms. (1 + 2sin α cos α) + 1 - sin 2α = 2 + 2sin α cos α - sin 2α

Step 5: Use a trigonometric identity. The double-angle identity for sine is: sin 2α = 2sin α cos α

Now substitute sin 2α in terms of 2sin α cos α:

2 + 2sin α cos α - sin 2α = 2 + 2sin α cos α - 2sin α cos α

Step 6: Simplify further. The terms 2sin α cos α and -2sin α cos α cancel each other out, leaving us with:

2

So the simplified expression is 2.