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
mafiozo [28]
1 year ago
13

Simplify using trigonometric identities 2sinθ - sin2θ cosθ

Mathematics
1 answer:
Anit [1.1K]1 year ago
8 0

Double angle identity for sine:

\sin(2x) = 2 \sin(x) \cos(x)

\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)

Factorize the left side.

2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)

Pythagorean identity:

\cos^2(x) + \sin^2(x) = 1

\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)

so that

\boxed{2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin^3(\theta)}

You might be interested in
A homeowner wants several small dormers built on his roof to admit light. They will be in the shape of isosceles triangles whose
Vlad1618 [11]
P = s + (s + 5) + (s + 5) This represents the two sides that are 5 inches longer than the base (s + 5) and the base (s).
Simplifying.
100 = 3s + 10
subtract 10 from both sides
 90 = 3s
divide both sides by 3
30 = s
base = 30
sides = 35

CHECK 30 + 35 + 35 = 100

4 0
3 years ago
3. Which rule best describes the last three numbers shown in the pattern? 10, 12, 9, 11​
sergij07 [2.7K]

Answer:

it goes by 2 two times then subtracts 3 then again

Step-by-step explanation:

10,12,9,11,8,10,7

5 0
3 years ago
Given that, 1 Chinese yuan = £0.11, convert £460 into Chinese yuan. Give your answer to the nearest yuan.
Ugo [173]

Answer:

i so want to know this aswell

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
How many 1 quart containers of milk did the cafeteria ues
user100 [1]
Pls provide the complete question.
6 0
3 years ago
Read 2 more answers
Find the volume of the composite figure. First, find the volume of the triangular prism. 4 cm Triangular prism Volume = [?] cm 5
crimeas [40]

Answer: See attached image.

6 0
2 years ago
Other questions:
  • Someone help me with this pls i will give brainliest
    8·2 answers
  • The cook needs to make the dough for 9 small pizzas. Each pizza dough needs cup of flour. How much flour does the cook need to m
    7·1 answer
  • How can i find the volume of this figure help please
    6·1 answer
  • Is the decimal terminating or repeating?<br> 0.3
    8·1 answer
  • There is a bag filled with 6 blue and 5 red marbles.
    5·1 answer
  • PLEASEE HELP!!
    7·1 answer
  • Celina and Richard spend a certain amount of money from their money box each month to buy plants.
    14·1 answer
  • Is the following statement true or false?<br> Parallel lines do not intersect.
    13·2 answers
  • A machine stamps 330 parts in 11 minutes. Find the unit rate in parts per hour.
    10·1 answer
  • Ava bought a new computer and is now
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!