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
lawyer [7]
2 years ago
7

If cos theta + sin theta = root 2 cos thetha prove that cos theta - sin theta = root 2 sin theta

Mathematics
1 answer:
artcher [175]2 years ago
3 0

Answer:

We have:

If:

Cos(θ) + Sin(θ) = √2*cos(θ)

We want to prove that:

Cos(θ) - Sin(θ) = √2*Sin(θ)

Well, let's start with the first relation:

Cos(θ) + Sin(θ) = √2*cos(θ)

Now we can subtract 2*Sin(θ) and we will get:

Cos(θ) + Sin(θ) - 2*Sin(θ) = √2*cos(θ) - 2*sin(θ)

Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)

Now, we also can rewrite the first equation as:

Cos(θ) + Sin(θ) = √2*cos(θ)

Cos(θ) - √2*cos(θ) = -  Sin(θ)

Cos(θ)*( 1 - √2) = -Sin(θ)

Cos(θ) = -Sin(θ)/( 1 - √2) = Sin(θ)/(- 1 + √2)

We can replace this in the right side of theequation:

Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)

Cos(θ) - Sin(θ) = √2* Sin(θ)/(- 1 + √2) - 2*sin(θ)

Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)

Now we have this:

√2/(- 1 + √2)) - 2 = a

if we multiply all by (-1  + √2) we get:

√2 - 2*(-1  + √2) = a*(-1  + √2)

√2  + 2 - 2*√2 =  a*(-1  + √2)

2 - √2 = a*(-1  + √2)

√2*(√2 - 1) = a*(-1  + √2)

√2*(√2 - 1)/(-1  + √2) = a

√2 = a

Then:

√2/(- 1 + √2)) - 2 = √2

If we replace this in the equation:

Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)

We get:

Cos(θ) - Sin(θ) = √2*Sin(θ)

Which is the thing we wanted to get.

You might be interested in
If the graph of the function moves to the right two units what is the new vertex of the function
Allisa [31]

Answer:

Let's talk through this a one step at a time.

*Since f(x) is concave-up with its vertex on the x-axis, we know f(x) ≥ 0.

*We also know that when we shift a function's domain by a positive number, we shift the function left and when we shift a function's domain by a negative number, we shift the function right. So f(x-5) is f(x) shifted to the right by 5.

*At this point, f(x-5) has its vertex at (5,0).

*When we negate f(x-5), the parabola becomes concave down yet the vertex remains at (5,0). Now we're at -f(x-5). At this point we have -f(x-5)≤0 with a range (-∞,0]

*If we add 2 to create g(x)=2-f(x-5), then we have a concave down parabola with its vertex shifted up by 2, at (5,2). So, g(x) is concave down with its vertex at (5,2). Hence

5 0
3 years ago
In golf your scores can be under or over par. If a golfer has 3 games in which he scores 3 under on the first, 5 over in the sec
tiny-mole [99]
(-3)+(5)+(-3)=-1
The awnser is -1.
5 0
2 years ago
He floor of a moving van is 3 feet off of the ground. The ramp into the van makes a 12° angle with the ground. About how long is
soldier1979 [14.2K]

Given :

Hight of the van from the ground, h = 3 feet.

The ramp into the van makes a 12° angle with the ground.

To Find :

How long is the ramp.

Solution :

Let, length of ramp is l .

So, height of ramp in terms of length is given by :

h = l \times sin\ 12^o\\\\l = \dfrac{h}{sin \ 12^o}\\\\l = \dfrac{3}{sin \ 12^o}\\\\l = 14.429 \ feet

Hence, this is the required solution.

8 0
2 years ago
Number 6. 1 moreee im stuck helpp
Andreyy89
B. V = (26.6)(4.6)
26.6 = l * w
7 0
2 years ago
Read 2 more answers
Student Council sells bottled water at the cheerleading completion. At this rate, how many cases of bottled water would they sel
amid [387]

Answer:

27

Step-by-step explanation:

Lets find the rate of selling:

Let v= the rate of selling, b = number of bottles of water, and t = time:

b over t gives us the v=\frac{b}{t}=\frac{3}{20}=\frac{6}{40}=0.15 rate of selling:

3 hours is 60min * 3 = 180 mins, and since v=b/t, vt=b:

(0.15) * 180 = 27 bottles of water

4 0
2 years ago
Other questions:
  • An angles measure is 6 degrees more than 3 times the measure of its complement. Find the measure of the angle.
    15·1 answer
  • Please Help...........................................................
    6·2 answers
  • the probability that your ticket will be chosen in a drawing is 6%. there are 250 tickets in the drawing. how many tickets are y
    13·2 answers
  • The value of a professional basketball player's autograph rose 40% in the last year. It is now worth $322.00. What was it worth
    13·1 answer
  • The average price for a gallon of gasoline in the country A is $3.71 and in country B it is $3.45. Assume these averages are the
    11·1 answer
  • Which equation shows the best estimate for 4,310 ÷ 72 using compatible numbers?
    11·2 answers
  • Joaquin buys white shirts for $12 each. after he dyes and paints each shirt he plans to sell them at a 65% markup Joaquin wants
    8·1 answer
  • A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th
    15·1 answer
  • WHOEVER ANSWERS THIS WILL GET BRAINLIEST!!! SERIOUS ANSWERS ONLY!!!
    8·1 answer
  • Observations of the center of the Milky Way show the presence of a super massive black hole with a mass of 4.6 x 106 solar masse
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!