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SOVA2 [1]
3 years ago
13

Find the value of in the triangle shown below. 2.5 2 6.5

Mathematics
1 answer:
frez [133]3 years ago
8 0

I have attached the complete question with the triangle.

Answer:

x = 6

Step-by-step explanation:

From the image attached we are told to find x in the triangle.

The triangle is a right angle triangle and so we can use pythagoras theorem to find x.

x² = 6.5² - 2.5²

x² = 42.25 - 6.25

x = √36

x = 6

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Verify the identity tan(???? − ????) = tan(????)−tan(????) / 1+tan (????) tan(????) for all (???? − ????) ≠ ???? / 2 + ????n.
Anna11 [10]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following identity:

tan(x-y) = \frac{tan x - tan y}{1 + tan x tan y}

So we need to begin with the definition of tan, we know that tan x = \frac{sin x}{cos x} and we have this:

tan (x-y) = \frac{sin(x-y)}{cos(x-y)}   (1)

We also have the following identities:

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

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

And if we apply those identities into equation (1) we got:

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

We can divide numerator and denominator from expression (2) by \frac{1}{cos x cos y} like this:

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

And if we simplity we got:

tan(x-y) = \frac{tan x - tan y}{tan x tan y +1 }

And with that we complete the proof. And that appies for all (x-y) \neq \frac{\pi}{2} +n\pi

6 0
4 years ago
Graph a line with a slope of 2/5 that contains the point (-2,4)
ZanzabumX [31]

y = mx + b

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4 = -4/5 + b

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24/5 = b

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Hope this helps! ;)

3 0
3 years ago
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3 years ago
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Determinati numarul b astfel incat : (4x8)^15 : 4^5:2^6=2^b si 3^4x3^5x3^17=3^b
Serhud [2]
The answer is 3 becasue 

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3 years ago
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What is the quotient of<br> 8.5<br> ——-<br> -0.5<br><br> A. O -17<br> B.1.7<br> C.17<br> D. -1.7
NARA [144]

Answer:

the answer is A) -17

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4 0
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