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4 years ago

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

Mathematics

1 answer:

Vaselesa [24]4 years ago

7 0

Answer:

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!)

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4 years ago

Y=3x-2

Inessa [10]

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a) $(x,y) = (3, 7)$ is a solution of the linear equation.

b) The rate of change of the equation is 3.

c) The y-intercept of the equation is -2.

d) Jayne is working in the grocery one day, according to her calculations, renting the lot costs 2 dollars per day and she could earn 3 dollars per hour by selling pastries. How much money does she earn after working 8 hours?

Step-by-step explanation:

a) If $(x,y) = (3, 7)$ is a solution of the linear equation, then $f(3) = 7$ . If $x = 3$ , then the function evaluated at this value is:

$y = 3\cdot (3) -2$

$y = 7$

Hence, $(x,y) = (3, 7)$ is a solution of the linear equation.

b) The rate of change of the equation is represented by the slope of the function, which is the constant that multiplies the indepedent variable ( $x$ ). Hence, the rate of change of the equation is 3.

c) The y-intercept of the equation is the only constant of the equation. Hence, the y-intercept of the equation is -2.

d) A real-world scenario would be the following: Jayne is working in the grocery one day, according to her calculations, renting the lot costs 2 dollars per day and she could earn 3 dollars per hour by selling pastries. How much money does she earn after working 8 hours?

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3 years ago