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
ehidna [41]
3 years ago
9

Derive these identities using the addition or subtraction formulas for sine or cosine: sinacosb=(sin(a+b)+sin(a-b))/2

Mathematics
1 answer:
Sergeu [11.5K]3 years ago
3 0

Answer:

The work is in the explanation.

Step-by-step explanation:

The sine addition identity is:

\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b).

The sine difference identity is:

\sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(a).

The cosine addition identity is:

\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b).

The cosine difference identity is:

\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b).

We need to find a way to put some or all of these together to get:

\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}.

So I do notice on the right hand side the \sin(a+b) and the \sin(a-b).

Let's start there then.

There is a plus sign in between them so let's add those together:

\sin(a+b)+\sin(a-b)

=[\sin(a+b)]+[\sin(a-b)]

=[\sin(a)\cos(b)+\cos(a)\sin(b)]+[\sin(a)\cos(b)-\cos(a)\sin(b)]

There are two pairs of like terms. I will gather them together so you can see it more clearly:

=[\sin(a)\cos(b)+\sin(a)\cos(b)]+[\cos(a)\sin(b)-\cos(a)\sin(b)]

=2\sin(a)\cos(b)+0

=2\sin(a)\cos(b)

So this implies:

\sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)

Divide both sides by 2:

\frac{\sin(a+b)+\sin(a-b)}{2}=\sin(a)\cos(b)

By the symmetric property we can write:

\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}

You might be interested in
Name the quadrant in which the point (-4, -3) could be found on the coordinate plane
lesantik [10]
On the negative plane field? because everything on the - side is negative.
5 0
3 years ago
Which of the following values cannot represent the side length of a triangle?
MissTica
The answer would be <span>6.5.12

A triangle couldn't be made if the total sum of the two shortest side is less than the longest side. In this case, the two shortest side would be 5 and 6. The longest side would be 12.
If you try to add the two lowest side, the result would be 5+6=11. That means even if you make the triangle with 179.99 degrees that the 5 and 6 look like a straight line, the longest side it can achieve is 11.</span>
7 0
3 years ago
Read 2 more answers
The inverse of f(x)=x^2 is also a function t/f
vodka [1.7K]

The Answer is false.

the function f (x) = x 2 is NOT one-to-one, and therefore cannot have an inverse.Therefore, the function f (x) = x 2 does NOT have an inverse.

3 0
3 years ago
Read 2 more answers
Given right triangle JKL what is the value of cos(L)?
NemiM [27]
For the right triangle to be given in name of three letters such as this, the right angle is most likely to be in the center, in this case letter K. To determine the common trigonometric properties of a certain angle we may use of the mnemonics SOH - CAH - TOA. 
                          sin angle = opposite side / hypotenuse
                          cosine angle = adjacent side / hypotenuse
                          tangent angle = opposite side / adjacent side

If we let small letter j, k, and l be the sides opposite to angles J, K, and L, respectively. Then, the cos (L) will be,
                                       cos (L) = j/k
8 0
3 years ago
Find two number closest to 5000 that are divisible by 36,21,and 12​
Pavlova-9 [17]
1,008 hope this helps
7 0
3 years ago
Other questions:
  • WILL MARK BRAINLIEST PLEASE HELP ASAP. The value of n is a distance of 1.5 units from -2 on a number line.
    14·2 answers
  • Please help. Due soon.
    15·1 answer
  • You have 16 digs for your current volleyball season. There are 3 games left in the season. You want to break your previous recor
    9·1 answer
  • What is the degree of the polynomial below?<br> x + 3 - 2x2 + 4x2 - 4x
    15·2 answers
  • What is the 100th term in the list?<br>10<br>17<br>24<br>31<br>38​
    9·1 answer
  • Daniel got 86% on his test and he solved 5 points extra credit problem. What would be his new grade on this test?
    15·1 answer
  • On what sum of money will the compound interest for 2 years at 8% p.a. will be ₹7448?​
    12·2 answers
  • The table shows the weight of bunches of bananas and the price of each bunch
    11·1 answer
  • The same survey database cited in exercise 4.3.1 (A-5) shows that 32 percent of U.S. adults indicated that they have been tested
    14·1 answer
  • L = 5t + 12
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!