Prove that cos(a-b) - cos(a+b) = 2sina sinb

Answers

Answer 1

Answer: We know:
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

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

L = cos(a)cos(b) + sin(a)sin(b) - (cos(a)cos(b) - sin(a)sin(b))

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

= 2sin(a)sin(b) = R

Related Questions

What is the answer to this proplem in the picture.
Write the definition of a function absoluteValue, that receives an integer parameter and returns the absolute value of the parameter's value. So, if the parameter's value is 7 or 803 or 141 the function returns 7, 803 or 141 respectively. But if the parameter's value is -22 or -57, the function returns 22 or 57 (same magnitude but a positive instead of a negative). And if the parameter's value is 0, the function returns 0.
Equation of the line (0,1),(2,5),(3,7)
The value of x is ____ °,and the value of y is____ °. this is really confusing help please..
X intercept2, y-intercept 1/3

The sales tax rate is 8%. Estimate the tax on a jacket that costs $69.95.

Answers

Answer:

8% is the same as (.08)x69.95=.556 or .56 ( because of rounding )

so .56 plus 69.95= $70.51

Step-by-step explanation:

Add 8% and 69.95 and then add 69.95 again to that answer and ta da!

According to the textbook, the median age in the United States is closest to 13. 23. 35. 49.

Answers

I can't find the answer tonight. I accidentally left my textbook in school.

4a² - 25? little help? Can you show me the steps to gets the answer? Thanks!

Answers

4a² - 25

= (2a)² - 5²

= (2a+5)(2a-5) since a² -b² = (a+b)(a-b)

This is simply a difference of squares. To factor this, you simply take the square roots of the leading coefficient and the C term. Thus you get 2 and 5. As a pair of factors, it is simply (2a+5)(2a-5). If you actually need to solve this, you can set either the factors or the original equation equal to 0.

Tom drives a truck. His regular trip is a distance of 280 km. He drives at an average speed of 80 km/h. For safety reasons Tom’s boss puts a speed limiter on his truck. This reduces Tom’s average speed by 10 km/h. How much longer will it take Tom to drive his regular trip?

Answers

280km at 80k/hr gives 3.5hrs.
280km at 10km/hr gives 28hrs.
therefore it will take him 28 - 3.5 = 24.5hrs longer.

Solve the system of equations; x - 2y = 2 and 3x - 5y = 9 by writing and solving a matrix equation. Show all your work.

Answers

y= $(28)/(11)$
x= $(3)/(11)$

Working;
Start by forming a matrix as shown below;
$\left[\begin{array}{ccc}1&-2\n3&5\end{array}\right] ( \left[\begin{array}{ccc}x\ny\end{array}\right])= ( \left[\begin{array}{ccc}2\n9\end{array}\right])$

Step II
Finding the inverse of the matrix as shown below;
Determinant;
(1*5)-(3*(-2)=11
Inverse;
$(1)/(11) \left[\begin{array}{ccc}5&2\n-3&1\end{array}\right] \left[\begin{array}{ccc}1&-2\n3&5\end{array}\right] \left[\begin{array}{ccc}x\ny\end{array}\right]= (1)/(11) \left[\begin{array}{ccc}5&2\n-3&1\end{array}\right] \left[\begin{array}{ccc}2\n9\end{array}\right]$

Evaluating further;
$(1)/(11) \left[\begin{array}{ccc}11&0\n0&11\end{array}\right] \left[\begin{array}{ccc}x\ny\end{array}\right] = (1)/(11) \left[\begin{array}{ccc}28\n3\end{array}\right]$

x= $(28)/(11) and y = (3)/(11)$

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?A.right 1 unit
B.left 1 unit
C.right 2 units
D.left 2 units

Answers

The vertex of f(x) = x^2 is (0,0)

The vertex of g(x) = x^2 + 2x + 1 = 0 is (-1,0)

Then, translating the f(x) one unit to the left will map (0,0) onto (-1,0).

Answer B: left 1 unit.

Answer: left 1 unit

Step-by-step explanation:

Edge 2021 also I’m in a big storm right now so if I’m not online in a few days you know why

Other Questions

A cinema seats 250 people. If 170 people are in the cinema, what percentage of the seats are filled? 42 54 75 68 55

what fraction of a clockwise revolution does the hour of a clock turn through when it goes from a) 4 to 7 b) 8 to 2 c) 1 to 10

Which of the following statements are true regarding functions? *Check all that applyA. The horizontal line test may be used to determine whether a function is one-to-one.B. A function is a relation in which each value of the input variable is paired with exactly one value of the output variable.C. The vertical line test may be used to determine whether a function is one-to-one.D. A sequence is a function whose domain is the set of real numbers.

Help please thanks so much