Question

Cos^2 3π/34 + cos^2 7π/17

Answer 1

Cos((pi/2) - (7*pi/17))^2 + Cos( (7*pi/17) )^2

Меняем на кофункцию Sin(X)

Sin (7*pi/17)^2 + Cos (7*pi/17)^2

Получаем тригонометрические единицу вида: Sin(X)^2 +Cos(X)^2 =1

ответ: 1

Answer 2

To simplify the expression cos^2(3π/34) + cos^2(7π/17), you can use trigonometric identities.

1. Recall the trigonometric identity: cos(θ) = cos(-θ)

This means that you can write cos(3π/34) as cos(-3π/34) and cos(7π/17) as cos(-7π/17).

2. Now, use the trigonometric identity for the square of the cosine: cos^2(θ) = 1/2 * (1 + cos(2θ))

So, applying this identity to both terms in your expression:

cos^2(-3π/34) = 1/2 * [1 + cos(2 * (-3π/34))] = 1/2 * [1 + cos(-3π/17)]

cos^2(-7π/17) = 1/2 * [1 + cos(2 * (-7π/17))] = 1/2 * [1 + cos(-14π/17)]

3. Now, use the fact that cos(-θ) = cos(θ) and apply it to both terms:

cos^2(-3π/17) = 1/2 * [1 + cos(3π/17)]

cos^2(-14π/17) = 1/2 * [1 + cos(14π/17)]

4. Finally, add the two simplified expressions together:

cos^2(3π/34) + cos^2(7π/17) = [1/2 * (1 + cos(3π/17))] + [1/2 * (1 + cos(14π/17))]

Now, you have a simplified expression for cos^2(3π/34) + cos^2(7π/17).