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
Nataly_w [17]
3 years ago
11

Tan(x+pi) + 2sin(x+pi)=0can you help prove this and make the left side equal the right?

Mathematics
1 answer:
vladimir1956 [14]3 years ago
5 0

This is not an identity but an equation. You're supposed to find the values of x for which this is true. It is *not* true for all values of x.

To see why:

\tan x has period \pi, which means \tan(x+\pi)=\tan x.

The angle sum identity for \sin x says that

\sin(x+\pi)=\sin x\cos \pi+\cos x\sin\pi=-\sin x

So

\tan(x+\pi)+2\sin(x+\pi)=\tan x-2\sin x

By definition of \tan x,

\tan x=\dfrac{\sin x}{\cos x}

and so

\tan x-2\sin x=\sin x\left(\dfrac1{\cos x}-2\right)

which is only 0 if either \sin x=0 (which only happens for certain values of x) or \dfrac1{\cos x}-2=0\implies\cos x=\dfrac12 (which also only happens for certain values of x). It's these values of x you want to find.

\sin x=0 whenever x is a multiple of \pi, i.e. x=n\pi for any integer n.

If 0\le x, then \cos x=\dfrac12 is true for x=\dfrac\pi3 and x=\dfrac{5\pi}3. Then to account for all other possible values, we add a multiple of 2\pi, so that x=\dfrac\pi3+2n\pi or x=\dfrac{5\pi}3+2n\pi for integers n.

You might be interested in
write the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x+y=-5. include your work in
Readme [11.4K]
Parallel to 2x+y=-5
2x+y-2x=-5-2x
y=-2x-5
y=mx+b
Slope: m=-2

As the line is parallel must have the same slope:
m=-2
And it has an x-intercept of 2: when x=2, y=0→Point: P1=(2,0)=(x1,y1)
x1=2, y1=0

y-y1=m(x-x1)
y-0=(-2)(x-2)
y=-2x+4
In standard form:
y+2x=-2x+2x+4
2x+y=4

Answer: The equation of the line, in standard form, that passes through the origin and is parallel to x+y=6 is x+y=0
6 0
3 years ago
Read 2 more answers
Evan has 2 pieces of wood: one is 90 inches and the other is 72 inches.he wants to cut both pieces of wood into smaller pieces s
Gre4nikov [31]

72/2=36

90/2=45

2+2=4 pieces of wood

6 0
3 years ago
I need help with this?
Dmitrij [34]

el triangulo que forma el radio es un triangulo equilátero y por lo tanto el lado del hexágono sera  de la misma medida que el radio:

lado = radio = 2 cm

como hay 6 lados, lo multiplicamos por 6 :

2x6 = 12 cm

entonces el perímetro del hexágono es 12 cm

Saludos¡

6 0
3 years ago
Read 2 more answers
Carla wants to create a garden in her backyard. She wants the width of the garden to be 9 meters and the area to be 162 meters.
Naddik [55]
<h3>Answer:  18</h3>

Work Shown:

area = length*width

length = area/width

length = 162/9

length = 18 meters

7 0
2 years ago
The following is an example of which property?
balu736 [363]

Answer:

I think it is commutative

Step-by-step explanation:

because commute means move so I think that's what it is

3 0
3 years ago
Read 2 more answers
Other questions:
  • how many gallons of 80% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 70% antifr
    10·1 answer
  • Write 60 divided 10 in three different ways
    9·1 answer
  • Suppose you are running a racing tournament with 12 horses. All eligible horses run in the race at once, and after the first rac
    15·1 answer
  • GIVING BRAINLIEST, FIVE STARS, AND THANKS FOR PROPER ANSWER AND CORRECT ANSWER CALLING ALL THE SMARTIES :D
    13·1 answer
  • Use the remainder theorem and the factor theorem to determine whether (y − 3) is a factor of (y4 + 2y2 − 4).
    12·2 answers
  • The owner of a garden center delivers bags of mulch. Each bag is sold for $6. The owner spends $16 for transportation to deliver
    13·1 answer
  • 9 + [10 + (5 - 4) x 2] please use pemdas and write 3 steps
    13·1 answer
  • 5x^5 + 20x^3 - 105.x^2<br>factor the following polynomial completely​
    10·1 answer
  • Uh... Answer this question for 50 points.<br> Thanks in advance- hopefully
    15·2 answers
  • Ahmed owns a land of breadth (x+7) units &amp;having an area of 2+ 14x + 49 sq. Units. (i)Find its length.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!