Question

Sin(30°+a)+cos(60°+a)=cos a

Answer 1

Ответ:

синус а косинус 30- синус 30 косинус а+ косинус 60 косинус а - синус 60 синус а== 1/2* корень из 3* синус а- 1/2 *косинус а + 1/2 * косинус а- 1/2 * корень из 3 * синус а= 0

2) АНАЛОГИЧНО

Объяснение:

Answer 2

To solve the equation sin(30°+a) + cos(60°+a) = cos(a), we can simplify each term using trigonometric identities.

Let's start by simplifying sin(30°+a): Using the angle sum identity for sine, sin(30°+a) = sin(30°)cos(a) + cos(30°)sin(a). Since sin(30°) = 1/2 and cos(30°) = √3/2, we can substitute these values: sin(30°+a) = (1/2)cos(a) + (√3/2)sin(a).

Next, let's simplify cos(60°+a): Using the angle sum identity for cosine, cos(60°+a) = cos(60°)cos(a) - sin(60°)sin(a). Since cos(60°) = 1/2 and sin(60°) = √3/2, we can substitute these values: cos(60°+a) = (1/2)cos(a) - (√3/2)sin(a).

Now, substituting these simplified expressions back into the original equation, we have: (1/2)cos(a) + (√3/2)sin(a) + (1/2)cos(a) - (√3/2)sin(a) = cos(a).

The terms with sin(a) cancel out, and we are left with: cos(a) = cos(a).

This equation is an identity, which means it holds true for all values of a. Therefore, the original equation sin(30°+a) + cos(60°+a) = cos(a) is satisfied for any value of a.