Question

Sin(60+a)+sin(a-60)упростить выражения помогите пожалуйста дам 12бпллов​

Answer 1

Ответ:

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

Answer 2

Simplifying the Expression sin(60+a) + sin(a-60)

To simplify the expression sin(60+a) + sin(a-60), we can use the sum-to-product identities for sine functions.

The sum-to-product identities for sine functions state that sin(A) + sin(B) = 2*sin((A+B)/2)*cos((A-B)/2) [[1]].

Using this identity, we can simplify the given expression.

Applying the Sum-to-Product Identity

Using the sum-to-product identity, we can simplify the expression sin(60+a) + sin(a-60) as follows:

sin(60+a) + sin(a-60) = 2*sin((60+a+a-60)/2)*cos((60+a-(a-60))/2)

Simplifying further:

= 2*sin((2a)/2)*cos(120/2) = 2*sin(a)*cos(60) = 2*sin(a)*(1/2) = sin(a)

Final Simplified Expression

After applying the sum-to-product identity, the simplified expression for sin(60+a) + sin(a-60) is sin(a).