Question

(sinальфа-cosальфа)^2-1+4*sin2альфа я

Answer 1

=sin^2a-2sinacosa+cos^2a-(sin^2a+cos^2a)+4(2sinacosa)=sin^2a-2sinacosa+cos^2a-sin^2a-cos^2a+8sinacosa=6sinacosa

Answer 2

The expression you provided, (sin(alpha) - cos(alpha))^2 - 1 + 4sin(2alpha), can be simplified further. Let's break it down step by step:

Step 1: Expand the square term: (sin(alpha) - cos(alpha))^2 = sin^2(alpha) - 2*sin(alpha)*cos(alpha) + cos^2(alpha)

Step 2: Simplify the trigonometric identity: sin^2(alpha) + cos^2(alpha) = 1

Step 3: Substitute the simplified identity into the expanded term: (sin(alpha) - cos(alpha))^2 = 1 - 2*sin(alpha)*cos(alpha)

Step 4: Simplify the expression by substituting sin(2alpha) with 2sin(alpha)cos(alpha): 4sin(2alpha) = 4 * 2sin(alpha)cos(alpha) = 8sin(alpha)*cos(alpha)

Now we can rewrite the expression using the simplified terms: (1 - 2*sin(alpha)cos(alpha)) - 1 + 8sin(alpha)*cos(alpha)

Further simplification may be possible depending on the context or specific values of alpha.