Question

Cos(2a-п/6)+cos(2a+п/6)​

Answer 1

Ответ:

Объяснение:

= 2cos((2a-p/6+2a+p/6)/2)*cos((2a-p/6-2a-p/6))/2= 2cos(2a)*cos(-p/6)=2*√3/2cos(2a)= √3cos(2a)

Answer 2

The expression you've provided is the sum of two cosine functions:

cos(2a - π/6) + cos(2a + π/6)

To simplify this expression, we can use the trigonometric identity:

cos(A) + cos(B) = 2 * cos((A + B) / 2) * cos((A - B) / 2)

In this case, let A = 2a + π/6 and B = π/6. Plugging these values into the identity:

2 * cos((2a + π/6 + π/6) / 2) * cos((2a + π/6 - π/6) / 2)

Simplifying the angles:

2 * cos((2a + π/3) / 2) * cos(2a / 2)

Further simplification:

2 * cos(a + π/6) * cos(a)

Now we can use another trigonometric identity:

cos(A + B) = cos(A) * cos(B) - sin(A) * sin(B)

Let A = a and B = π/6:

cos(a + π/6) = cos(a) * cos(π/6) - sin(a) * sin(π/6)

cos(π/6) = √3 / 2 and sin(π/6) = 1 / 2:

cos(a + π/6) = √3/2 * cos(a) - 1/2 * sin(a)

Substitute this back into the expression:

2 * (√3/2 * cos(a) - 1/2 * sin(a)) * cos(a)

Simplify:

√3 * cos(a) - sin(a) * cos(a)

So, the simplified form of the given expression is:

√3 * cos(a) - sin(a) * cos(a)