Question

√2*соs^2*7pi/12-√2*sin^2*7pi/12

Answer 1

cos^2 a - sin^2 a = cos 2a, поэтому

V2*(cos^2 (7pi/12) - sin^2 (7pi/12)) = V2*cos (7pi/6) = V2*(-V3/2) = - V6/2

Answer 2

To simplify the expression √2 * cos^2(7π/12) - √2 * sin^2(7π/12), we can use the trigonometric identity:

cos(2θ) = cos^2(θ) - sin^2(θ)

Applying this identity, we have:

√2 * cos^2(7π/12) - √2 * sin^2(7π/12) = √2 * cos(2 * 7π/12)

Now, let's find the value of cos(2 * 7π/12):

cos(2 * 7π/12) = cos(7π/6)

The value of cos(7π/6) can be determined from the unit circle or memorized trigonometric values. It is -√3/2.

Substituting this value back into our expression:

√2 * cos^2(7π/12) - √2 * sin^2(7π/12) = √2 * (-√3/2) = -√6/2 = -√6/2

So the simplified value of the expression is -√6/2.