Solve for x: sinx-cosx=√2

1 answer:

6 0

sinx - cosx =sqrt(2)
Taking square on both sides:
(sinx - cosx)^2 =sqrt(2)^2
sin^2(x) -2cos(x)sin(x) + cos^2(x) = 2
Rearranging the equation:
sin^2(x)+cos^2(x) -2cos(x)sin(x)=2
As,
sin^2(x)+cos^2(x) = 1
So,
1-2sinxcosx=2
1-1-2sinxcosx=2-1
-2sinxcosx = 1
Using Trignometric identities:
-2(0.5(sin(x+x)+sin(x-x))=1
-sin2x+sin0=1
As,
sin 0 = 0
So,
sin2x+0 = -1
sin2x = -1
2x=-90 degrees + t360
Dividing by 2 on both sides:
x=-45 degrees + t180
or 2x=270 degrees +t360
x= 135 degrees + t180 where t is integer

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Jill and Erika made 5 gallons of lemonade for their lemonade stand. How many quarts did they make? If they charge $2.50 per quar

yawa3891 [41]

a. How many quarts did they make is 25 quarts of lemonade

b. How much money will they make if they sell it all is $62.50

a. Calculation to determine How many quarts did they make.

Given: 1 gallon =5 quarts

Hence:

5 gallons of lemonade=5×5 quarts of lemonade

5 gallons of lemonade=25 quarts of lemonade

b. Calculation to determine how much money will they make if they sell it all

Given: 1 quarts=$2.50