Question

Cos(2П-2x)-sin(3П/2+6x)/-4cos(П-4x) Упростить ​

Answer 1

Ответ:

Пошаговое объяснение:

cos(2π - 2x) - sin(3π/2 + 6x)/ ( - 4cos(π - 4x)) = cos2x - ( - cos6x/4cosx) = (4cos4x · cos2x + cos6x) : 4cos4x =( 2(cos2x + cos6x) + cos6x) : 4cos4x = (2cos2x + 2cos6x + cos6x) : 4cos4x =

= (2cos2x + 3cos6x): 4cos4x

Answer 2

To simplify the expression, let's break it down step by step:

1. Recall the trigonometric identities:

   • cos(2π - θ) = cos(θ)
   • sin(π/2 + θ) = cos(θ)

2. Apply the above identities to the given expression: cos(2π - 2x) - sin(3π/2 + 6x) / -4cos(π - 4x) = cos(2x) - cos(3π/2 + 6x) / -4cos(π - 4x)

3. Convert sin(3π/2 + 6x) to cos(θ) using the identity sin(θ) = cos(π/2 - θ): cos(2x) - cos(π/2 - (3π/2 + 6x)) / -4cos(π - 4x) = cos(2x) - cos(-π/2 - 6x) / -4cos(π - 4x)

4. Since cos(-θ) = cos(θ), we can simplify further: cos(2x) - cos(π/2 + 6x) / -4cos(π - 4x)

5. Use the identity sin(θ) = cos(π/2 - θ) to convert cos(π/2 + 6x) to sin(-6x): cos(2x) - sin(-6x) / -4cos(π - 4x)

6. Since sin(-θ) = -sin(θ), we get: cos(2x) + sin(6x) / 4cos(π - 4x)

The simplified expression is: cos(2x) + sin(6x) / 4cos(π - 4x)