Question

(cosa + sina)^2-sin2α

Answer 1

Ответ:

1

Пошаговое объяснение:

Cos(a)2+2cos(a)sin(a)+sin(a)2-sin(2a)=1+sin(2a)-sin(2a)=1

Answer 2

To simplify the expression $(\cos \alpha + \sin \alpha)^2 - \sin 2\alpha$, you can use trigonometric identities. Here's how you can do it step by step:

1. Start with the expression: $(\cos \alpha + \sin \alpha)^2 - \sin 2\alpha$

2. Expand the square of the binomial $(\cos \alpha + \sin \alpha)^2$: $(\cos \alpha + \sin \alpha)(\cos \alpha + \sin \alpha) - \sin 2\alpha$

3. Use the distributive property to expand the expression: $\cos^2 \alpha + 2\cos \alpha \sin \alpha + \sin^2 \alpha - \sin 2\alpha$

4. Use the Pythagorean trigonometric identity $\sin^2 \alpha + \cos^2 \alpha = 1$ to simplify $\cos^2 \alpha + \sin^2 \alpha$ to 1: $1 + 2\cos \alpha \sin \alpha - \sin 2\alpha$

5. Use the double angle identity for sine: $\sin 2\alpha = 2\sin \alpha \cos \alpha$: $1 + 2\cos \alpha \sin \alpha - 2\sin \alpha \cos \alpha$

6. Now, you can factor out a common term of $\sin \alpha \cos \alpha$: $1 + \sin \alpha \cos \alpha$

So, $(\cos \alpha + \sin \alpha)^2 - \sin 2\alpha$ simplifies to $1 + \sin \alpha \cos \alpha$.