Question

1-(Cosa-Sina)^2 сократить

Answer 1

1-(cosα-sinα)²=1-(cos²α-2sinαcosα+sin²α)=1-(1-2sinαcosα)=1-1-2sinαcosα=-2sinαcosα=-sin2α

Answer 2

To simplify the expression 1 - (cosθ - sinθ)^2, we can expand the square and then simplify.

Expanding the square:

1 - (cosθ - sinθ)^2 = 1 - (cosθ - sinθ)(cosθ - sinθ)

Using the formula for the square of a binomial, which is (a - b)(a - b) = a^2 - 2ab + b^2, we can expand the expression further:

= 1 - (cosθ)^2 + 2cosθsinθ - (sinθ)^2

= 1 - cos^2θ + 2cosθsinθ - sin^2θ

Now, using the trigonometric identity cos^2θ + sin^2θ = 1, we can substitute that in the expression:

= 1 - 1 + 2cosθsinθ

= 2cosθsinθ

So, the simplified form of the expression 1 - (cosθ - sinθ)^2 is 2cosθsinθ.