Verify sin^4 x - sin^2 x = cos^4 x - cos^2 x is an identity

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

sin(x)^4 - sin(x)^2 = cos(x)^4 - cos(x)^2

sin(x)^2 = 1 - cos(x)^2:

sin(x)^4 - 1 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2

-(1 - cos(x)^2) = cos(x)^2 - 1:

cos(x)^2 - 1 + sin(x)^4 = ^?cos(x)^4 - cos(x)^2

sin(x)^4 = (sin(x)^2)^2 = (1 - cos(x)^2)^2:

-1 + cos(x)^2 + (1 - cos(x)^2)^2 = ^?cos(x)^4 - cos(x)^2

(1 - cos(x)^2)^2 = 1 - 2 cos(x)^2 + cos(x)^4:

-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = ^?cos(x)^4 - cos(x)^2

-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = cos(x)^4 - cos(x)^2:

cos(x)^4 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2

The left hand side and right hand side are identical:

 (identity has been verified)

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

answer is 12345678900987654321234567890987654321

step-by-step explanation: