1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kolbaska11 [484]
3 years ago
14

If alpha and beta be 2 distinct roots satisfying equation a cos theta+bsin theta=c,Show that cos (alpha+beta)=(a^2-b^2)/(a^2+b^2

)
Mathematics
1 answer:
garri49 [273]3 years ago
8 0
Cos(α+β)=cosα∗cosβ−sinα∗sinβ

acosθ+bsinθ=c

acosθ=c−bsinθ

Square both sides

a2(1−sinθ)=c2+b2sin2θ−2∗c∗b∗sinθ

(b2+a2)sin2θ−2∗c∗b∗sinθ+c2−a2=0

Product of Roots =ca

sinα∗sinβ=c2−a2a2+b2

Now use similar method to have an equation in terms of cos2θ

acosθ+bsinθ=c

acosθ−c=−bsinθ

a2cos2θ+c2−2∗a∗ccosθ=b2(1−cos2θ)

(a2+b2)cos2θ−2∗a∗cosθ∗c+c2−b2=0

Product of Roots =ca

cosα∗cosβ=c2−b2a2+b2

Now substitute the values in First Equation 

cos(α+β)=cosα∗cosβ−sinα∗sinβ

⟹c2−b2+a2−c2a2+b2

⟹a2−b2a2+b2


You might be interested in
Tanisha's mother buys 38 lemons. They know it takes 8 lemons to make 80 oz. of lemonade. Does Tanisha need more lemons? If not,
Cloud [144]
She has extra because she only wants to make 80oz and it takes 8 and she has 30 so 30 is extra
7 0
3 years ago
The greens want to put an additional on their house 18 months from now they will need to save 10620 in order to achieve this goa
GREYUIT [131]

Answer:

sbebebvdevevevsvsvevwvwvwwvevev

6 0
3 years ago
Tree factories build the same widget. Th number of widgets produced in each factory are shown in the table.
masya89 [10]

Answer:

1 8 9 6

y= 3x

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
I’LL GIVE YA BRAINLESS!! I need the answer ASAP
navik [9.2K]

Answer:

55% because 1815 divided by 3300 is .55, and .55 is 55%

8 0
3 years ago
-21+(-59) what is the answer
Lemur [1.5K]

Answer:

-80

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • A circular rug has a diameter of 6 feet. What is the area of the rug?
    10·2 answers
  • A glacier flows at a rate of 20 meters per day. What is the flow rate in kilometers per year?
    12·1 answer
  • Find the value of two number if their difference is 11 and the sum is 55
    9·1 answer
  • What is the coefficient of 10x+100
    13·2 answers
  • Solve for the indicated variable.<br> 8y + 7x = 9 for x
    9·2 answers
  • 5. Write an equation for a line with a slope of -4 and goes through the point (5, -1). Show all work.​
    10·1 answer
  • Keith has landscaping bricks that are 0.75 feet long.
    5·1 answer
  • What is 2, 3, 4?????????
    9·1 answer
  • I need help with these problems please
    13·1 answer
  • Simplify (2m^6)^3.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!