Question

Cos²a-1=?(sina+cosa)²-2sinacosa=?​

Answer 1

Ответ:

решение смотри на фотографии

Объяснение:

Answer 2

$1) \; cos^2a-1=-(1-cos^2a)=-sin^2a\\\\\\2)\; (sina+cosa)^2-2sinacosa=\\\\=sin^2a+2sinacosa+cos^2a-2sinacosa\\\\=sin^2a+cos^2a=1$

Answer 3

Let's break down the expressions step by step:

1. Cos²a - 1: This is the trigonometric identity for the cosine squared angle minus 1: cos²(a) - 1 = -sin²(a).

2. (sina + cosa)² - 2sin(a)cos(a): This expression involves the sum of sines and cosines squared, along with a term involving sine and cosine multiplication.

   • (sina + cosa)² can be expanded using the trigonometric identity: (sina + cosa)² = sin²(a) + 2sin(a)cos(a) + cos²(a).
   • Substituting this expansion into the expression, we get: sin²(a) + 2sin(a)cos(a) + cos²(a) - 2sin(a)cos(a).

Now, let's simplify this expression further:

• sin²(a) + cos²(a) is a trigonometric identity that equals 1.
• Therefore, the expression simplifies to: 1 + 0, which is just 1.

So, (sina + cosa)² - 2sin(a)cos(a) simplifies to 1.

To summarize:

• Cos²a - 1 simplifies to -sin²a.
• (sina + cosa)² - 2sin(a)cos(a) simplifies to 1.