Question

Cos B - sin B sin 2B​

Answer 1

Ответ:

Объяснение:

cosb-sinb×sin2b=

cosb-sinb×2×sinb×cosb=

cosb-2×sin^2b×cosb=

cosb(1-2sin^2 b)=

cosb×cos2b

Answer 2

To simplify the expression "Cos B - sin B sin 2B," we'll apply trigonometric identities to transform it into a simpler form.

Let's use the double-angle identity for sine: sin(2B) = 2 * sin(B) * cos(B)

Now, the expression becomes: Cos B - sin B * 2 * sin B * cos B

Next, we'll factor out common terms: Cos B - 2 * sin^2(B) * cos(B)

Finally, we can use the Pythagorean identity for sine and cosine: sin^2(B) + cos^2(B) = 1

Rearranging the Pythagorean identity: sin^2(B) = 1 - cos^2(B)

Substitute this into the expression: Cos B - 2 * (1 - cos^2(B)) * cos(B)

Expand the expression: Cos B - 2 * (cos^3(B) - cos(B))

Now, combine like terms: Cos B + 2 * cos(B) - 2 * cos^3(B)

Factor out cos(B): cos(B) * (1 + 2 - 2 * cos^2(B))

Simplify further: cos(B) * (3 - 2 * cos^2(B))

So, the simplified expression is: cos(B) * (3 - 2 * cos^2(B))