Question

(sin^2 п/8 - cos^2 п/8)^2 Как решить?

Answer 1

Используя формулу для косинуса двойного аргумента
 cos2a=cos^2 a-sin^2 a,   получаем
(- cos 2*π/8)^2 =(-cos π/4)^2=(- √2 /2)^2 =2/4=1/2 =0.5 Ответ 0.5

Answer 2

Π/8=22.5°=0.5*45
sin22.5=√((1-1/√2)/2) => sin^2(22.5)=(1-1/√2)/2 (пусть)=а
cos22.5=√((1+1/√2)/2) => cos^2(22.5)=(1+1/√2)/2 (пусть)=b
Подставляем (а-b)^2= a^2-2ab+b^2
a^2=1-(√2)+1/2=0.5-√2
ab= (1-1/2)/4= 0.125
b^2= 1+(√2)+1/2=0.5+√2
Суммируем и получаем 1.125

Answer 3

Solving the Expression (sin^2 π/8 - cos^2 π/8)^2

To solve the given expression (sin^2 π/8 - cos^2 π/8)^2, we can start by using trigonometric identities to simplify the expression.

The trigonometric identity sin^2(x) - cos^2(x) = -cos(2x) can be used to simplify the given expression.

Applying this identity, we get: (sin^2 π/8 - cos^2 π/8)^2 = (-cos(2*π/8))^2

Now, we can simplify further by evaluating -cos(2*π/8): -cos(2*π/8) = -cos(π/4)

Using the trigonometric values for cos(π/4), we find: cos(π/4) = 1/√2

Therefore, the expression simplifies to: (-cos(π/4))^2 = (-1/√2)^2 = 1/2

So, the value of the given expression (sin^2 π/8 - cos^2 π/8)^2 is 1/2.