Question

2√3соs^2 17П/12-2√3син^2 17П/12​

Answer 1

.............................

Answer 2

To simplify the given expression, we'll use the trigonometric identity:

cos^2θ - sin^2θ = cos(2θ).

Substitute θ = 17π/12 into the identity:

cos^2(17π/12) - sin^2(17π/12) = cos(2 * 17π/12).

Now, we need to find the cosine of 2 * (17π/12):

Let's recall that cos(θ) = cos(-θ). So, we can rewrite 2 * (17π/12) as -2 * (-17π/12):

cos(2 * (17π/12)) = cos(-2 * (-17π/12)).

Now, we can use the double-angle formula for cosine:

cos(2θ) = cos^2θ - sin^2θ.

cos(-2θ) = cos^2θ - sin^2θ.

So, in our case:

cos(-2 * (17π/12)) = cos^2(17π/12) - sin^2(17π/12).

Now, the expression becomes:

2√3 * (cos^2(17π/12) - sin^2(17π/12)).

Finally, using the double-angle identity again:

2√3 * cos(-2 * (17π/12)) = 2√3 * cos(17π/6) = 2√3 * (sqrt(3)/2) = 3.

So, the simplified expression is 3.