Question

2 cos^2 13П/24 cos^2 23П/24​

Answer 1

$2Cos^{2} \frac{13\pi }{24}Cos^{2} \frac{23\pi }{24} =2Cos^{2}(\frac{\pi }{2}+\frac{\pi }{24})Cos^{2}(\pi-\frac{\pi }{24})=2Sin^{2}\frac{\pi }{24}Cos^{2}\frac{\pi }{24}=0,5Sin^{2}\frac{\pi }{12}$

Answer 2

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

cos(π - θ) = -cos(θ)

Let's apply this identity to the given expression:

2 * cos^2(13π/24) * cos^2(23π/24)

Using the identity cos(θ) * cos(θ) = cos^2(θ), we can rewrite the expression as:

2 * (cos(13π/24) * cos(13π/24)) * (cos(23π/24) * cos(23π/24))

Now, let's use the identity cos(θ) * cos(π - θ) = -sin(θ) * sin(θ) = -sin^2(θ):

2 * (-sin^2(13π/24)) * (-sin^2(11π/24))

Next, we can use the identity sin(π - θ) = sin(θ):

2 * (-sin^2(13π/24)) * (-sin^2(π - 13π/24))

Now, we can simplify the expression:

2 * (-sin^2(13π/24)) * (-sin^2(π/24))

Finally, using the identity sin^2(θ) = 1 - cos^2(θ), we get:

2 * (1 - cos^2(13π/24)) * (1 - cos^2(π/24))

Now, you can further simplify the expression by evaluating the cosines at their respective angles and perform the calculations. Note that π (pi) is approximately 3.14159.