Question

(cosa+sina)^2-2sinacosa

Answer 1

Ответ:

$(cos\alpha + sin\alpha)^{2} - 2sin\alpha cos\alpha = cos^{2}\alpha + 2sin\alpha cos\alpha + sin^{2}\alpha - 2sin\alpha cos\alpha = cos^{2} \alpha + sin^{2}\alpha = 1$

Answer 2

To simplify the expression $(\cos a + \sin a)^2 - 2\sin a \cos a$, you can expand and simplify it step by step.

1. Start by squaring the expression $\cos a + \sin a$:

$(\cos a + \sin a)^2 = \cos^2 a + 2\cos a \sin a + \sin^2 a$

2. Now, use the trigonometric identity $\sin^2 a + \cos^2 a = 1$:

$\cos^2 a + 2\cos a \sin a + \sin^2 a = 1 + 2\cos a \sin a$

3. Finally, subtract $2\sin a \cos a$ from the expression:

$1 + 2\cos a \sin a - 2\sin a \cos a$

4. Combine like terms (the last two terms cancel each other out):

$1$

So, the simplified expression is $1$.