Cos (7п/5-a) cos(2п/5+а)+sin(7п/5-a) sin(2п/5+а)

Предыдущий
вопрос Следующий
вопрос

This expression can be simplified using the trigonometric identity:

cos(A-B) = cosA cosB + sinA sinB

Applying this identity to the given expression, we get:

= cos(7π/5) cos(2π/5) + sin(7π/5) sin(2π/5)

Now, we can evaluate the cosine and sine values at the respective angles using the unit circle or trigonometric values. Let's simplify further:

cos(7π/5) = cos(π + 2π/5) = -cos(2π/5)
sin(7π/5) = sin(π + 2π/5) = sin(2π/5)

Substitute these values back into the expression:

= -cos(2π/5) cos(2π/5) + sin(2π/5) sin(2π/5)

Now, use the trigonometric identity sin^2(x) + cos^2(x) = 1:

= -cos^2(2π/5) + sin^2(2π/5)
= -(1 - sin^2(2π/5)) + sin^2(2π/5)
= -1 + sin^2(2π/5) + sin^2(2π/5)
= -1 + 2sin^2(2π/5)

Therefore, the simplified expression is -1 + 2sin^2(2π/5).