Question

Sin⁴ 23π/12- cos⁴13π\12​

Answer 1

Ответ:

-1

Пошаговое объяснение:

0^4/12-(-1)^4

0/12-1

0-1

-1

Answer 2

To calculate sin^4(23π/12) - cos^4(13π/12), you can use trigonometric identities to simplify the expression.

First, let's simplify each term separately:

1. sin^4(23π/12):

Recall that sin(π/12) = sin(π/6)/2 = (√3/2)/2 = √3/4.

sin(23π/12) is in the fourth quadrant, so it's equal to -sin(π/12).

sin^4(23π/12) = (-√3/4)^4 = (3/16).

2. cos^4(13π/12):

cos(π/12) = cos(π/6)/2 = (√3/2)/2 = √3/4.

cos(13π/12) is in the fourth quadrant, so it's equal to cos(π/12).

cos^4(13π/12) = (√3/4)^4 = (3/16).

Now, subtract the two values:

sin^4(23π/12) - cos^4(13π/12) = (3/16) - (3/16) = 0.

So, sin^4(23π/12) - cos^4(13π/12) is equal to 0.