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
Pani-rosa [81]
3 years ago
9

Prove the identity (cosx+cosy)^2+(sinx-siny)^2= 2+2cos(x+y)

Mathematics
2 answers:
muminat3 years ago
8 0
TRIGONOMETRIC \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: RESOLUTIONS \\ \\ \\\\Given \: expression \: - \\ \\ \\ { (\cos(x) + \cos(y)} )^{2} + ( {( \sin(x ) - \sin(y) )}^{2} \\ \\ = { \cos(x) }^{2} + { \cos(y) }^{2} + 2 \cos(x) \cos(y) \\ \: \: \:+\: \: { \sin(x) }^{2} + { \sin(y) }^{2} - 2 \sin(x) \sin(y) \\ \\ = { \cos(x) }^{2} \: + { \sin(x) }^{2} + \\ \: \: \: \: \: { \cos(y) }^{2} + { \sin(x) }^{2} \: + \\ \: \: \: \: \: 2( \cos(x) \cos(y) - \sin(x) \sin(y) ) \\ \\ = \: 1 + 1 + 2( \cos(x + y) ) \\ \\ Using \:Trigonometric \: Identities \: - \\ \\ { \sin(q) }^{2} + { \cos(q) }^{2} = \: 1 \: \\ \cos(x) \cos(y) - \sin(x) \sin(y) = \cos(x + y) \\ \\ \\ \\ { (\cos(x) + \cos(y)} )^{2} + ( {( \sin(x ) - \sin(y) )}^{2} \\ = 2 + 2( \cos(x + y) ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: Ans.\\ \\
astra-53 [7]3 years ago
4 0
(cos(x) + cos(y))^2 + (sin(x) - sin(y))^2 Remove the brackets

cos^2(x)
+ cos^2(y) + 2cos(x)*cos(y) + sin^2(x) - 2(sin(x)*sin(y) + sin^2(y) Combine these two in bold to make 1 because sin^2(x) + cos^2(x) = 1

1 + cos^2(y) + 2cos(x)*cos(y) - 2*sin(x)*cos(y) + sin^2(y) 
These two in bold also make 1

2 + 2cos(x)*cos(y) - 2*sin(X)*sin(y) Bring out a common factor of 2
2 +2(cos(x)*cos(y) -  sin(x)*sin(y) )

but cos(x+y ) = cos(x)*cos(y) - sin(x)*sin(y)

2 + 2* cos(x + y) is your final answer. 

You might be interested in
Please help, preferably in the next half an hour.
scoundrel [369]

Answer:

For the first question the correct form would be B. It would be 6(p-3)=42. For the second question the answer would be 10.

Step-by-step explanation:

For the first question B is correct because it's 3 dollars off which would be -3.

For the second question you would multiply 6 with p and 6 with -3. This would equal to 6p-18. This would make the equation 6p-18=42. You would then add 18 to 42, which equals 60. Finally you would divide 60 by 6, which equals 10, which is your answer.

7 0
2 years ago
What is the arc measure in degrees pls help
11111nata11111 [884]
An ARC measure is an angle of ARC makes at the top of a circle where as the ARC links is a span along the ARC
7 0
3 years ago
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side
lorasvet [3.4K]

Answer:

Step-by-step explanation:

1.

cot x sec⁴ x = cot x+2 tan x +tan³x

L.H.S = cot x sec⁴x

       =cot x (sec²x)²

       =cot x (1+tan²x)²     [ ∵ sec²x=1+tan²x]

       =  cot x(1+ 2 tan²x +tan⁴x)

       =cot x+ 2 cot x tan²x+cot x tan⁴x

        =cot x +2 tan x + tan³x        [ ∵cot x tan x =\frac{ \textrm{tan x }}{\textrm{tan x}} =1]

       =R.H.S

2.

(sin x)(tan x cos x - cot x cos x)=1-2 cos²x

 L.H.S =(sin x)(tan x cos x - cot x cos x)

          = sin x tan x cos x - sin x cot x cos x

           =\textrm{sin x cos x }\times\frac{\textrm{sin x}}{\textrm{cos x} } - \textrm{sinx}\times\frac{\textrm{cos x}}{\textrm{sin x}}\times \textrm{cos x}

           = sin²x -cos²x

           =1-cos²x-cos²x

           =1-2 cos²x

           =R.H.S

         

3.

1+ sec²x sin²x =sec²x

L.H.S =1+ sec²x sin²x

         =1+\frac{{sin^2x}}{cos^2x}                       [\textrm{sec x}=\frac{1}{\textrm{cos x}}]

         =1+tan²x                        [\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}]

         =sec²x

        =R.H.S

4.

\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}} = \textrm{2 csc x}

L.H.S=\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}}

       =\frac{\textrm{sinx(1+cos x)+{\textrm{sinx(1-cos x)}}}}{\textrm{(1-cos x)\textrm{(1+cos x})}}

      =\frac{\textrm{sinx+sin xcos x+{\textrm{sinx-sin xcos x}}}}{{(1-cos ^2x)}}

     =\frac{\textrm{2sin x}}{sin^2 x}

      = 2 csc x

    = R.H.S

5.

-tan²x + sec²x=1

L.H.S=-tan²x + sec²x

        = sec²x-tan²x

        =\frac{1}{cos^2x} -\frac{sin^2x}{cos^2x}

        =\frac{1- sin^2x}{cos^2x}

        =\frac{cos^2x}{cos^2x}

        =1

     

       

8 0
3 years ago
60% of what number is 21
Lerok [7]
60% of 35 is 21 

Change the percentage (60) into a decimal by dividing it over 100:
\frac{60}{100} = 0.6

Divide 21 by the decimal:
<span>\frac{21}{0.6} = 35</span>
3 0
3 years ago
Read 2 more answers
For a regular n-gon:
snow_lady [41]
I believe the sum of the interior angles is the number of sides (n), subtracted by 2, and multiplied by 180.
(n - 2) x 180 = sum of interior angles of a n-gon

I also believe that the sum of exterior angles of a n-gon equals to 360 degrees.
3 0
2 years ago
Other questions:
  • Given f(x) = -2x + 7, evaluate for f(10)
    7·2 answers
  • Algebra
    7·1 answer
  • Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th b
    8·2 answers
  • A grocery store sells Swiss cheese for $5.90 a pound. To the nearest cent what is the cost oer ounce if Swiss cheese? round you
    6·2 answers
  • Keisha has 10 coins.Two of the coins are nickels,6 pennies,and the rest are dimes.What is the value of Keisha's coins?
    5·2 answers
  • A random sample of n=25 individuals is selected from a population with μ=20 , and a treatment is administered to each individual
    8·1 answer
  • Round 73,588 ten thousand
    10·2 answers
  • A triangle has the following side lengths: 4cm, 4cm, and 4cm. What kind of triangle is it?
    8·2 answers
  • Please help me please!!!
    7·1 answer
  • Shona bought 5 bags of cement and 4 bags of gravel. The total weight of her bags was 200 kilograms.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!