Question

(sina-cosa)^2+2sin2a/1-sin^2*2a

Answer 1

Пошаговое объяснение:

(sina+cosa)^2-sin2a=1

sin²a+2*sin*cos+cos²2-sin2a=1

sin²2+sin2a+cos²a-sin2a=1

sin²2+cos²a=1

1=1

Answer 2

Let's simplify the expression step by step:

1. Recall the trigonometric identity: sin(2a) = 2sin(a)cos(a).

2. Rewrite the expression using the identity above:

(sin(a) - cos(a))^2 + 2sin(2a) / (1 - sin^2(2a))

3. Expand the squared term:

(sin^2(a) - 2sin(a)cos(a) + cos^2(a)) + 2sin(2a) / (1 - sin^2(2a))

4. Since sin^2(a) + cos^2(a) = 1 (trigonometric identity), the expression becomes:

(1 - 2sin(a)cos(a)) + 2sin(2a) / (1 - sin^2(2a))

5. Now, use the identity sin(2a) = 2sin(a)cos(a) again:

(1 - 2sin(a)cos(a)) + 2(2sin(a)cos(a)) / (1 - sin^2(2a))

6. Combine the terms:

1 - 2sin(a)cos(a) + 4sin(a)cos(a) / (1 - sin^2(2a))

7. Simplify further:

1 + 2sin(a)cos(a) / (1 - sin^2(2a))

There you have it, the simplified expression is 1 + 2sin(a)cos(a) / (1 - sin^2(2a)).