Question

Sin(30+a)-cos(60+a)=

Answer 1

Ответ: √3 * sin(a)

Решение на фото.

Answer 2

To simplify the expression sin(30 + a) - cos(60 + a), you can use trigonometric identities and angle addition formulas.

1. Start by simplifying sin(30 + a):

sin(30 + a) = sin(30)cos(a) + cos(30)sin(a)

Now, you need to find the values of sin(30) and cos(30).

sin(30 degrees) = 1/2 cos(30 degrees) = √3/2

So, the expression becomes:

(1/2)cos(a) + (√3/2)sin(a)

2. Next, simplify cos(60 + a):

cos(60 + a) = cos(60)cos(a) - sin(60)sin(a)

Now, find the values of cos(60) and sin(60):

cos(60 degrees) = 1/2 sin(60 degrees) = √3/2

So, the expression becomes:

(1/2)cos(a) - (√3/2)sin(a)

3. Now, subtract the second expression from the first:

(sin(30 + a) - cos(60 + a)) = [(1/2)cos(a) + (√3/2)sin(a)] - [(1/2)cos(a) - (√3/2)sin(a)]

Now, distribute the negative sign on the right side:

(sin(30 + a) - cos(60 + a)) = (1/2)cos(a) + (√3/2)sin(a) - (1/2)cos(a) + (√3/2)sin(a)

4. Simplify further by canceling out like terms:

(sin(30 + a) - cos(60 + a)) = (1/2)cos(a) - (1/2)cos(a) + (√3/2)sin(a) + (√3/2)sin(a)

(sin(30 + a) - cos(60 + a)) = 0 + (√3/2)sin(a) + (√3/2)sin(a)

5. Finally, combine like terms:

(sin(30 + a) - cos(60 + a)) = 2(√3/2)sin(a)

(sin(30 + a) - cos(60 + a)) = √3sin(a)

So, the simplified expression is √3sin(a).