Sin2a-cos2a+cos4a/cos2a-sin2a+sin4a

Предыдущий
вопрос Следующий
вопрос

Let's simplify the expression step by step.

Given expression: (sin2a - cos2a + cos4a) / (cos2a - sin2a + sin4a)

First, let's simplify the numerator:
sin2a - cos2a + cos4a

Using the trigonometric identity sin^2(x) + cos^2(x) = 1
=> sin^2(2a) = 1 - cos^2(2a) = 1 - (1 - sin^2(2a)) = sin^2(2a)

Therefore, sin2a - cos2a = sin^2(2a) - cos^2(2a) = sin^2(2a) - (1 - sin^2(2a)) = 2sin^2(2a) - 1

Now, the numerator becomes: 2sin^2(2a) - 1 + cos(4a)

Next, let's simplify the denominator:
cos2a - sin2a + sin4a

sin4a = 2sin(2a)cos(2a)
cos2a - sin2a + sin4a = cos2a - sin2a + 2sin(2a)cos(2a)

Now, let's simplify the expression:
(cos2a - sin2a + 2sin(2a)cos(2a))

Using trigonometric identities:
cos(2a) = cos^2(a) - sin^2(a) and sin(2a) = 2sin(a)cos(a)

=> cos2a - sin2a + 2sin(2a)cos(2a) = cos^2(a) - sin^2(a) - sin^2(a) + 2sin(a)cos(a)2sin(a)cos(a)
= cos^2(a) - 2sin^2(a) + 2sin(a)cos(a)2sin(a)cos(a)
= cos^2(a) - 2sin^2(a) + 2sin(a)cos(a)2sin(a)cos(a)

Therefore, the denominator becomes:
cos^2(a) - 2sin^2(a) + 2sin(a)cos(a)2sin(a)cos(a)

Now the expression becomes:
(2sin^2(2a) - 1 + cos(4a)) / (cos^2(a) - 2sin^2(a) + 2sin(a)cos(a)2sin(a)cos(a))

Further simplification may not yield a single value solution.