answersLogoWhite

0


Best Answer

There is a hint to how to solve this in what is required to be shown: a and b are both squared.

If

  1. a cos θ + b sin θ = 8
  2. a sin θ - b cos θ = 5

then square both sides of each to get:

  1. a² cos² θ + 2ab cos θ sin θ + b² sin² θ = 64
  2. a² sin² θ - 2ab sin θ cos θ + b² cos² θ = 25

Now add the two together:

a² cos² θ + a² sin² θ + b² sin² θ + b² cos² θ = 89

→ a²(cos² θ + sin² θ) + b² (sin² θ + cos² θ) = 89

using cos² θ + sin² θ = 1

→ a² + b² = 89

User Avatar

Wiki User

โˆ™ 2018-04-13 06:57:15
This answer is:
๐Ÿ™
0
๐Ÿคจ
0
๐Ÿ˜ฎ
0
User Avatar

Add your answer:

Earn +20 pts
Q: If a cos theta plus b sin theta equals 8 and a sin theta - b cos theta equals 5 show that a squared plus b squared equals 89?
Write your answer...
Submit
Related questions

How would you solve and show work for cos2 theta if cos squared theta equals 1 and theta is in the 4th quadrant?

cos2(theta) = 1 cos2(theta) + sin2(theta) = 1 so sin2(theta) = 0 cos(2*theta) = cos2(theta) - sin2(theta) = 1 - 0 = 1


What is theta when tantheta plus sectheta equals 1 please show work?

copy this and paste in your browsers address window http://www.wolframalpha.com/input/?i=tan+theta+%2B+sec+theta+%3D1


How do you make a cross symbol on your keyboard?

you have to find the key with the plus and equals symbol. Then push the shift key and the plus/equals key. The "cross" should show up. Plus (+) equals (=). The plus should be above the equals.


How do you show X times x equals x squared?

It is: x*x = x2


How would you show all work for 1 minus 2cos squared theta?

You could not.1 - 2cos2theta is an expression which cannot be solved nor evaluated without information about theta. If you need to show its equivalence to another expression then it is necessary to know what the other expression is.


What is 12 plus 2?

fourteen. (14) If you need to count, let me show you. (12) plus equals


Integrate sqrt of 10000 divided by pi minus x squared plus sqrt of pi plus one twentieth and show work?

It's about 34 and a third


What are the Pythagorean identities?

There are three of them. Granted this means that there are different variations of all three. I'll show you the variations as well. This is coming straight from my Math 1060 (Trigonometry) notebook. Sorry there is no key to represent the angle; Theta.1. Sin2 (of Theta) + Cos2 (of Theta)= 1Variations: Sin2 (of Theta) = 1- Cos2 (of Theta)AND: Cos2 (of Theta) = 1-Sin2 (of Theta)2. Tan2 (of Theta) + 1 = sec2 (of Theta)Variations: Tan2 (of Theta) = Sec2 (of Theta) -13. 1 + Cot2 (of Theta) = Csc2 (of Theta)Variations: Cot2 (of Theta) = Csc2 (of Theta) -1


How can you show your work to solving the equation of 5x-2y equals -10 3x plus 6y equals 66?

There are 2 unknowns


Show a plus b divided 2 equals 2ab divided by a plus b?

b/2=2ab/+b means112.5


How do you show how sin theta equals cos theta tan theta?

sinθ = O/H cosθ = A/H tanθ = O/A cosθ*tanθ = A/H * O/A = AO/AH = O/H Therefore, sinθ = cosθtanθ = O/H (Notes: O=opposite, A=adjacent, H=hypotenuse)


What is the answer of this show the solution 2x-y equals 3 -x plus 2y equals -6?

x = 0 & y = -3


If z equals yf x2 - y2 show that ydz divided by dx plus xdz divided by dy equals xz divided by y?

4


Verify that Cos theta cot theta plus sin theta equals csc theta?

It's easiest to show all of the work (explanations/identities), and x represents theta. cosxcotx + sinx = cscx cosx times cosx/sinx + sinx = csc x (Quotient Identity) cosx2 /sinx + sinx = csc x (multiplied) 1-sinx2/sinx + sinx = csc x (Pythagorean Identity) 1/sinx - sinx2/sinx + sinx = csc x (seperate fraction) 1/sinx -sinx + sinx = csc x (canceled) 1/sinx = csc x (cancelled) csc x =csc x (Reciprocal Identity)


Beta theta pi grip?

You become intitiated into Beta Theta Pi and they will show you. Why dont you give it a try before you get misinformed, try the wrong grip, and get beat down.


How could an estimate show you that 362.9 plus 42.8 plus 35.46 equals 826.36 is wrong?

360 + 40 + 35 = 435, nowhere close to 826.


How do you graph the line x plus y equals 3 on the Cartesian Plane?

bend over and ill show you


What is the word equation to show the reaction between potassium carbonate and dilute hydrochloric acid?

Potassium carbonate plus hydrochloric acid equals potassium chloride plus carbon dioxide plus water.


6 boxes of nails. Each box has 123 nails. show the best way to use rounding to estimate the total number of nails.A 6200 equals 1200 B 6100 equals 600 C6 plus 200 equals 206 D 6 plus 100 equals 10?

B. 6 x 100 = 600


What does (show work) 12 plus 15h -14h plus 4 equals?

The expression: 12+15h-14h+4 can be simplified to 16+h by combining like terms


4y-4 plus y plus 24 equals 6y plus 20-4Y equals Need to show process?

Algebra4y-4 plus y plus 24 equals 6y plus 20-4YCombine like terms5y+20=2y+20Isolate Y3y=0y=0


What is 1 over 8 3?

Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals", "squared", "cubed" etc.The question does not show any operator between 1/8 and 3.Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals", "squared", "cubed" etc.The question does not show any operator between 1/8 and 3.Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals", "squared", "cubed" etc.The question does not show any operator between 1/8 and 3.Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals", "squared", "cubed" etc.The question does not show any operator between 1/8 and 3.


Can somebody show me the solution of this equation .6E plus E equal 20million?

the answer is E equals to 12.5 but i dont know how it came up with it.


7 minus 1 plus 6 equals show your work?

7-1=6 6+6=12


How do you show your work for x plus 8 equals 35?

If x+8 = 35 then x = 35-8 and so x = 27

Study guides

๐Ÿ““
Create a Study Guide