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
Eduardwww [97]
3 years ago
14

Prove Sin3theta = 3sintheta - 4sin^3theta

Mathematics
1 answer:
trapecia [35]3 years ago
3 0

Express the left hand side as

sin3theta=sin(theta+2theta)

now expand the right side of this equation using color(blue)"Addition formula"

color(red)(|bar(ul(color(white)(a/a)color(black)(sin(A±B)=sinAcosB±cosAsinB)color(white)(a/a)|)))

rArrsin(theta+2theta)=sinthetacos2theta+costhetasin2theta.......(A)

color(red)(|bar(ul(color(white)(a/a)color(black)(cos2theta=cos^2theta-sin^2theta=2cos^2theta-1=1-2sin^2theta)color(white)(a/a)|)))

The right hand side is expressed only in terms of sintheta's

so we use cos2theta=1-2sin^2theta........(1)

color(red)(|bar(ul(color(white)(a/a)color(black)(sin2theta=2sinthetacostheta)color(white)(a/a)|)))........(2)

Replace cos2theta" and " sin2theta by the expansions (1) and (2)
into (A)

sin(theta+2theta)=sinthetacolor(red)((1-2sin^2theta))+costhetacolor(red)((2sinthetacostheta)

and expanding brackets gives.

sin(theta+2theta)=sintheta-2sin^3theta+2sinthetacos^2theta....(B)

color(red)(|bar(ul(color(white)(a/a)color(black)(cos^2theta+sin^2theta=1rArrcos^2theta=1-sin^2theta)color(white)(a/a)|)))

Replace cos^2theta=1-sin^2theta" into (B)"

rArrsin(theta+2theta)=sintheta-2sin^3theta+2sintheta(1-sin^2theta)

and expanding 2nd bracket gives.

sin(theta+2sintheta)=sintheta-2sin^3theta+2sintheta-2sin^3theta

Finally, collecting like terms.

sin3theta=3sintheta-4sin^3theta="R.H.S hence proven"
You might be interested in
Krystal and 4 friends were going to the movies. Each ticket cost $12. They bought 2 buckets of popcorn at $4.50 each and then ea
Crazy boy [7]

so each ticket costs 12 dollars multiply that bye 5 you get 60

each bucket of popcorn costs 4.50 then multiply that bye 2 you get 9

then all five girls get a soda which costs 4.75 so you would multiply 4.75 bye 5 which is 23.75

so in total  you would get B.92.75

8 0
3 years ago
Read 2 more answers
Solve the inequality 3x - 5 < 4.
lbvjy [14]
<span>3x - 5 < 4.

Add 5 to both sides, 
3x < 9

Divide 3 from both sides, 
x < 3

Hope this helps!</span>
6 0
3 years ago
Read 2 more answers
1
Xelga [282]

Answer:

y = \dfrac{1}{2}x-4

Step-by-step explanation:

<h2>Equation of line in slope y-intercept form:</h2>

       \sf slope = m =\dfrac{1}{2}\\\\Point (2, -3) ; x_1 = 2 \ \& y_1 = -3\\\\\boxed{\bf y - y_1 =m(x -x_1)}

         \sf y - [-3] = \dfrac{1}{2}(x - 2)\\\\y + 3 =  \dfrac{1}{2}x - 2*\dfrac{1}{2}\\\\y + 3 = \dfrac{1}{2}x-1\\\\

                \sf y = \dfrac{1}{2}x - 1 - 3\\\\ y =\dfrac{1}{2}x-4

6 0
2 years ago
Which number is a counting number? Can you do both of them plz
DochEvi [55]
Question 3 is: D. All integers are rational numbers.
Question 4 is: C. the counting number is 4. Hope this helped :)
4 0
3 years ago
A line passes through the points (2,4) and (5,6) . Select Yes or No to tell whether each equation describes this line. Equation
krek1111 [17]

\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{6}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-4}{5-2}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{2}{3}(x-2)

3 0
3 years ago
Other questions:
  • If it were possible to eat a hamburger every minute of every day without stopping how many years would it take to eat a billion
    11·1 answer
  • Write an equation that can be used to find the atmospheric temperature T, at an altitude A.
    7·1 answer
  • Pls need this last thing due also 9/24/18
    14·1 answer
  • What is the radius of a circle with an area of 66 yards squared? Round to the nearest tenth of a yard.
    13·2 answers
  • What is the answerto c and d
    13·1 answer
  • Which choice is equivalent to the product below?<br> ..<br> Someone pls help
    5·1 answer
  • Find the area of the sector in<br> terms of pi.<br> 270°<br> 12<br> Area = [?]
    5·1 answer
  • Helpppppppppppp WILL MARK BRAINLIST
    15·1 answer
  • The equation of a curve is y = a^x
    15·1 answer
  • Solve. 3/4x + 6 = 33<br><br> explain the work please :,)
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!