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lutik1710 [3]
3 years ago
11

Prove the identity. tan(x − y) + tan(z − x) + tan(y − z) = tan(x − y) tan(z − x) tan(y − z)

Mathematics
1 answer:
Viktor [21]3 years ago
4 0

Step-by-step explanation:

This is known as the triple tangent identity.  Start with the fact that the three angles add up to 0.

(x − y) + (z − x) + (y − z) = 0

Subtract two terms to the other side and take the tangent:

x − y = -((z − x) + (y − z))

tan(x − y) = tan(-((z − x) + (y − z)))

Use reflection property:

tan(x − y) = -tan((z − x) + (y − z))

Now use angle sum identity:

tan(x − y) = -[tan(z − x) + tan(y − z)] / [1 − tan(z − x) tan(y − z)]

tan(x − y) = [tan(z − x) + tan(y − z)] / [tan(z − x) tan(y − z) − 1]

tan(x − y) [tan(z − x) tan(y − z) − 1] = tan(z − x) + tan(y − z)

tan(x − y) tan(z − x) tan(y − z) − tan(x − y) = tan(z − x) + tan(y − z)

tan(x − y) tan(z − x) tan(y − z) = tan(x − y) + tan(z − x) + tan(y − z)

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I will give Brainliest!!
sergey [27]

The value of y in the triangle is 6°.

<h3>How to calculate the value of y in the triangle?</h3>

Firstly, it's important to note that a triangle has the total angles of 180°.

Based on the information, the triangle has interior angle measures of 11y, 10y + 10°, and 10y - 16º.

The value of y in the triangle will be illustrated thus:

11y + 10y + 10 + 10y - 16 = 180

31y - 6 = 180

31y = 180 + 6.

31y = 186

Divide.

y = 186 / 31

y = 6

The value of y is 6.

Learn more about triangles on:

brainly.com/question/17335144

#SPJ1

5 0
1 year ago
14 times the difference of 8 and w
Lunna [17]
14(8-W)=0
(14*8)-(14*W)=0
112-14W=0
-112 -112
------------------- The answer is 8
-14W= -112
-14W/(-14)= -112/(-14)
W=8
5 0
3 years ago
A square room has a perimeter of 40 feet. What is the area of the room?
Trava [24]

Answer:

100 ft²

Step-by-step explanation:

There are 4 congruent sides in a square

Perimeter = 4x

40 = 4x

x = 10

Area = base x height or length x width

Since all sides are the same, 10 is base and height

10x10 = 100

units = ft²

Answer = 100 ft²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

4 0
2 years ago
Read 2 more answers
Select the function that represents the simple interest formula
solniwko [45]

Answer:

its function a because im doing the same thing ur doing rn so what i got on that question was a because it would fit in with the formula the most

Step-by-step explanation:

3 0
2 years ago
Seriously someone help me i answered it but i don’t know if it is right so please tell me if it is and how i got the answer or p
alex41 [277]

Answer:

<h2>C</h2>

Step-by-step explanation:

To determine a function rule, look at the table. Input the x and y value from one column into the function to see if it is correct.

<h3>Function a: y = 10 - 2x</h3>

Input values

22 = 10 - 2(6)

22 = 10 - 12

22 ≠ -2 ❌

As we can see, function a gives us a false statement, so a is incorrect.

<h3>Function b: y = 2 - 10x</h3>

Input values

22 = 2 - 10(6)

22 = 2 - 60

22 ≠ -58 ❌

We once again get a false answer, so b is also not correct.

<h3>Function c: y = 10 + 2x</h3>

Input values

22 = 10 + 2(6)

22 = 22 ✔

Finally, we get a true statement, so option c is correct.

<h3>Function d: y = 2 + 10x</h3>

Just to check that option c is correct, we need to prove that d is incorrect.

Input values

22 = 2 + 60

22 ≠ 62 ❌

This is also wrong, so that proves that c is correct.

I'm always happy to help :)

6 0
3 years ago
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