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
IgorLugansk [536]
3 years ago
5

Express in terms of trig functions of single x : (sin2x+cos2x)^2

Mathematics
1 answer:
RSB [31]3 years ago
6 0

(\sin 2 x+\cos 2 x)^{2}=1+\sin 4 x

Solution:

Given trigonometric function:

(\sin 2 x+\cos 2 x)^{2}

Using perfect square formula:

(a+b)^{2}=a^{2}+2 a b+b^{2}

a=\sin 2 x, b=\cos 2 x

(\sin 2 x+\cos 2 x)^{2}=\sin ^{2}(2 x)+2 \sin 2 x \cos 2 x+\cos ^{2}(2 x)

Arranging square terms together.

                           =\sin ^{2}(2 x)+\cos ^{2}(2 x)+2 \sin 2 x \cos 2 x

Using the trigonometric identity: \sin ^{2}x+\cos ^{2}x=1

                           =1+2 \cos 2 x \sin 2 x

Using the trigonometric identity: 2 \cos   \sin x=\sin 2 x

                          =1+\sin (2 \cdot 2 x)

                          =1+\sin 4 x

Hence (\sin 2 x+\cos 2 x)^{2}=1+\sin 4 x.

You might be interested in
Arrange the following units in order from smallest to greatest: centimeter, kilometer, meter, millimeter
tatuchka [14]
Millimeter, centimeter, meter, kilometer.
3 0
3 years ago
Read 2 more answers
Give the coordinate of the point halfway between 2,1 and 2,4
frozen [14]
(2, 2.5) is exactly halfway
8 0
3 years ago
Please help meee!!! 5 stars to the best answer.
vovikov84 [41]

Answer:

3 cm

Step-by-step explanation:

First, find the volume of the cone.

V = \frac{1}{3}\pir²h

V = \frac{1}{3}(3.14)(9)(12)

V = 113.04

This means the sphere is also 113.04

Use the formula V = \frac{4}{3}\pir³

113.04 = \frac{4}{3}(3.14)r³

113.04 = 4.19r³

26.98 = r³

3 ≈ r

6 0
3 years ago
Read 2 more answers
A group of friends chartered a deep-sea fishing boat out of Destin, FL. The graph below represents the total cost, in dollars, o
liq [111]

Answer:

D: $26.25 I just took the assessment and got it right

5 0
3 years ago
Read 2 more answers
The points (2, 3) and (6, 11) lie on a line. What is the slope of this line?
AveGali [126]

Answer:

8/4

Step-by-step explanation:

to do slope is y2 - y1 over x2 - x1, so it would be 11 - 3 for 8, then 6 - 2, leaving 8/4.

3 0
3 years ago
Other questions:
  • Jacks Car averages 31.5 miles on the highway per gallon. If his fuel tank holds 13.2 gallons and it is 3/4 full then how far can
    14·1 answer
  • To find the area under the standard normal distribution curve between two z values, one first finds the difference between the t
    6·1 answer
  • The number of people waiting in a line to buy tickets x minutes after a ticket booth opened is given by the expression 70−5x .
    8·2 answers
  • If a^1/n=r then which of the following statements are true
    11·2 answers
  • What's name the reciprocal of 7​
    10·2 answers
  • There our 5 fish in a tank 3 of them drown and 2 of them swam away how many our left?
    15·2 answers
  • A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5? *
    10·1 answer
  • Brooke went to the hardware store and bought 20 identical copper pipes. When Brooke lined up the pipes end-to-end, the line was
    15·1 answer
  • What is the value of x??<br> −3(x+9)=33
    6·2 answers
  • Use the interval notation to express the solution -6x&gt;42​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!