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
Natasha2012 [34]
3 years ago
12

[Please, help me. I need it quickly]If cosA+sinA=√2, then prove A=45°.

Mathematics
1 answer:
Dmitrij [34]3 years ago
6 0

Step-by-step explanation:

Start by squaring both sides

cosA+sinA=\sqrt{2}

cos^2A+2cosAsinA+sin^2A=2

Apply Trig identity

cos^2x+sin^2x=1

2cosAsinA+1=2

2cosAsinA=1

Apply Trig Identity

2cosxsinx=sin(2x)

sin(2A)=1

2A=arcsin1

arcsin(1) is a known value \frac{\pi }{2}

2A=\frac{\pi }{2}

A=\frac{\pi }{4}

\pi radians=180^o

A=\frac{180^o}{4}=45^o

You might be interested in
If the area of a floor is 6 and the legnth is x and the width is x+1 then find the legnth and width
ELEN [110]
If x=2
length=2
width=2+1
=3

length × width = area
2×3=6

the answer for length is 2 ,while for the width is 3
5 0
4 years ago
Read 2 more answers
Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $27
kobusy [5.1K]

Answer:

y = 50x+25

f(x) = 50x+25

Step-by-step explanation:

Using the slope intercept form of the equation, y = mx+b

where x is the amount per day and b is the flat fee

2 days

125 = 2x+b

5 days

275 = 5x+b  

Subtract

275 = 4x+b  

125 = 2x+b

---------------------

150 = 3x

Divide by 3

150/3 = 3x/3

50 =x

The cost per day is 50 dollars

y = 50x +b

Using the data for 2 days

125 = 50*2 +b

125 = 100 +b

125-100 = b

b = 25

The equation is y = 50x+25

f(x) = 50x+25

To graph, The x axis is number of days and the y axis is total cost

The number of days starts with 0, which is the y intercept

Let x = 0, y =25

Using the slope, we go 50 up and 1 to the right ( 50 dollars per day)

The next point plotted ins ( 1,50)

Draw a straight line

4 0
3 years ago
Read 2 more answers
The coefficient of x in -7xy is -7​
Oksanka [162]

Answer:

True: the leading coefficient in the monomial is -7

Step-by-step explanation:

Math

5 0
3 years ago
A helicopter blade spins 775 times in 3 minutes. find the rate of the revolutions per second.
Stolb23 [73]
Use the proportions property:

775 times   ---------- 180 sec
  x               ----------    1 sec

x=\frac{775}{180}=4.3 \ times \ per \ sec
3 0
3 years ago
The number of pages that Ana, Hillary, Roger, and Juan can read in a day is shown below: Ana read 15% of her 46-page book.
dolphi86 [110]
The answer is D. Juan
8 0
3 years ago
Read 2 more answers
Other questions:
  • Identify any values of data that might affect the statistical measures of spread and center.
    13·1 answer
  • If an 18-day single payment loan has a periodic interest rate of 9.6%, what is the approximate APR of the loan? Show your work.
    14·1 answer
  • A 45 gm tube of 1% clotrimazole cream is combined with 15gm of base. What is the new % strength ?
    8·2 answers
  • A right triangle has legs of 12 ft and 16 ft. Find the longest side of the triangle. I don't get this at all :( help please
    9·2 answers
  • What is the equivalent fraction of 13/15 PLEASE show WORK
    15·1 answer
  • 4 friends earned $5.20 for washing a car.they shared the money equally. how much did each friend get
    10·1 answer
  • 1) w(x) = 3x + 1; Find w{-4- x)
    14·2 answers
  • What's the surface area of the pyramid?
    15·2 answers
  • Slope if (5,6) and (-7,5)
    14·1 answer
  • Which two triangles are congruent
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!