Question

Answer it for brainliest

Answer 1

new to the app mark as brainliest

Answer 2

Answer:

1/12

Step-by-step explanation:

f₄(x) = 1/4 (sin⁴ x + cos⁴ x)

f₆(x) = 1/6 (sin⁶ x + cos⁶ x)

f₄(x) - f₆(x) =  1/4 (sin⁴ x + cos⁴ x) -  1/6 (sin⁶ x + cos⁶ x)

f₄(x) - f₆(x) = 1/4 [ (sin²x + cos²x)² - 2 sin²x cos²x]  - 1/6 [ (sin²x + cos²x)³ - 3sin²x cos²x (sin²x + cos²x)]

Now, sin²x + cos²x = 1

f₄(x) - f₆(x) = 1/4 [1 - 2 sin²x cos²x] - 1/6 [ 1 - 3sin²x cos²x ]

f₄(x) - f₆(x) =  1/4 -1/2 sin²x cos²x - 1/6 + 1/2 sin²x cos²x

f₄(x) - f₆(x) =  1/4 -1/6

f₄(x) - f₆(x) = 1/12