How do i prove
sin^2 x cos^2 y - cos^2 x sin^2 y ≡ sin^2 x - sin^2 y

see below

Step-by-step explanation:

prove: sin²x cos²y - cos²x sin²y ≡ sin²x - sin²y

we notice that the Right side only has sin² functions, hence we can start by trying to remove the cos² functions from the Left side.

Recall the identity: sin²α + cos²α = 1 , can be rearranged to give us:

cos²α = 1 - sin²a.

If we apply this to the left side of our equation, then

cos²y = 1-sin²y, and cos²x = 1-sin²x

Substituting these into the left side of the equation:

sin²x cos²y - cos²x sin²y

= sin²x (1-sin²y) - (1-sin²x ) sin²y

= sin²x - (sin²x sin²y) - sin²y + (sin²x sin²y)

= sin²x  - sin²y

= Right Side of equation (Proven!)

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3