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3 years ago

Prove the following identity. [sin(x+y)+sin(x-y)]/[cos(x+y)+cos(x-y)] = tan(x)

1 answer:

4 0

$\frac{sin(x + y) + sin(x - y)}{cos(x + y) + cos(x - y)} = tan(x)$
$\frac{(sin(x)cos(y) + cos(x)sin(y)) + (sin(x)cos(y) - cos(x)sin(y))}{(cos(x)cos(y) - sin(x)sin(y)) + (cos(x)cos(y) + sin(x)sin(y))} = tan(x)$
$\frac{(sin(x)cos(y) + sin(x)cos(y)) + (cos(x)sin(y) - cos(x)sin(y))}{(cos(x)cos(y) + cos(x)cos(y)) + (-sin(x)sin(y) + (sin(x)sin(y))} = tan(x)$
$\frac{2sin(x)cos(y)}{2cos(x)cos(y)} = tan(x)$
$\frac{sin(x)}{cos(x)} = tan(x)$

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11111nata11111 [884]

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7 0

3 years ago

Read 2 more answers

An architect measures a beam to be 96.55 centimeters long, with an accuracy of plus or minus 0.02 centimeter. Which equation can

olga2289 [7]

Answer:

|96.55−0.02|= x

|96.55+0.02|=x

Step-by-step explanation:

Given that:

Measured length of beam = 96.55 cm

Measurement accuracy = plus or minus (± 0.02cm)

Limits of actual length of the beam:

Let limit of actual length = x

Lower limit :

|measured length - accuracy| = x

|96.55 - 0.02| = x

96.53) x

Upper limit :

|measured length + accuracy| = x

|96.55 + 0.02| = x

96.57 = x

3 0

3 years ago

A cube is painted so that one side is blue, two sides are red, and three sides are green. How many different such cubes can be p

Angelina_Jolie [31]

Answer:

So there are 3 distinct cubes.

Step-by-step explanation:

There are total six sides of the cube.

if we observe the given data and fix the sides of the cube by the color

So,

let suppose,

Blue color is painted on the top side of the cube

Now, we have left 5 sides

as per the information 2 sides are painted by Red color

let suppose,

1 Red color is painted on bottom side And 1 is on side

Now, we have left 3 sides

And 3 sides are green as per the given information.

1 green color painted on the adjacent side of the red side

1 green side is opposite of red side.

and 1 opposite of green side.

Now all side are colored and if we observe the above scenario

All other possibilities can be rotated to one of these.

So there are 3 distinct cubes.

8 0

3 years ago

the price of silver has increased by 15% per year from 2000. in the year 2000, harry bought a silver bowl for $190. which of the

lesya [120]

<h2>Answer</h2>

f(x) = 190(1.15)x

<h2>Explanation</h2>

To solve this, we are going to use the standard exponential function:

$f(x)=a(1+b)^x$

Where

$f(x)$ is the final price after $x$ years

$a$ is the initial price

$b$ is the rate in decimal form

$x$ is the time in years

We know from our problem that the initial price is $190, so $a=190$ . Now to convert the rate, 15%, to decimal form, we are going to divide it by 100%, so $r=\frac{15}{100} =0.15$ . Let's replace the values: