(cos П/12 - sin П/12)*(cos^3 П/12 + sin^3 П/12)

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вопрос

Let's simplify the expression step by step:

(cos(π/12) - sin(π/12))*(cos^3(π/12) + sin^3(π/12))

First, let's expand the terms using the trigonometric identities:

cos^3(π/12) = (cos(π/12))^3
sin^3(π/12) = (sin(π/12))^3

Now, we have:

(cos(π/12) - sin(π/12))*(cos(π/12))^3 + (sin(π/12))^3)

Next, we can distribute the terms:

(cos(π/12)cos^3(π/12) - sin(π/12)cos^3(π/12) + cos(π/12)sin^3(π/12) - sin(π/12)sin^3(π/12))

Simplify each term:

cos(π/12)cos^3(π/12) = cos^4(π/12)
-sin(π/12)cos^3(π/12) = -sin(π/12)cos^3(π/12)
cos(π/12)sin^3(π/12) = cos(π/12)sin^3(π/12)
-sin(π/12)sin^3(π/12) = -sin^4(π/12)

Putting it all together:

cos^4(π/12) - sin(π/12)cos^3(π/12) + cos(π/12)sin^3(π/12) - sin^4(π/12)

Therefore, the simplified expression is:

cos^4(π/12) - sin^4(π/12) + cos(π/12)sin^3(π/12) - sin(π/12)cos^3(π/12)