Question

Sin^2 альфа+cos:2 альфа

Answer 1

Ответ:

=1

Пошаговое объяснение:

Answer 2

It seems like you want to simplify the expression: sin^2(α) + cos(2α).

To do that, we can use trigonometric identities.

1. We know that sin^2(α) + cos^2(α) = 1 (the Pythagorean trigonometric identity).

2. We also know the double-angle identity for cosine: cos(2α) = 2cos^2(α) - 1.

Now, let's substitute the second identity into the expression:

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

Now, let's use the Pythagorean trigonometric identity (sin^2(α) + cos^2(α) = 1) to replace sin^2(α) with 1 - cos^2(α):

(1 - cos^2(α)) + (2cos^2(α) - 1)

Now, simplify:

1 - cos^2(α) + 2cos^2(α) - 1

Combine like terms:

(1 - 1) - cos^2(α) + 2cos^2(α)

0 - cos^2(α) + 2cos^2(α)

Now, simplify further:

2cos^2(α) - cos^2(α)

This simplifies to:

cos^2(α)

So, sin^2(α) + cos(2α) simplifies to cos^2(α).