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iren [92.7K]
3 years ago
10

Use the identity tan(theta) = sin(theta) / cos(theta) to show that tan(???? + ????) = tan(????)+tan(????) / 1−tan(????) tan(????

)
.
Mathematics
1 answer:
VMariaS [17]3 years ago
8 0

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following indentity:

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

So we need to begin with the definition of tangent, we know that tan (x) =\frac{sin(x)}{cos(x)} and we can do 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)= cos(a) cos(b) - sin(a) sin(b)

Now we can apply those identities into equation (1) like this:

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

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

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

And simplifying we got:

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

And that complete the proof.

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Tommy earned ​$ on Monday and ​$ on Tuesday. How many lucky bamboo plants can he buy with the total money he​ earned? lucky bamb
Montano1993 [528]

Answer: See explanation

Step-by-step explanation:

Your question isn't complete. But let's assume that the amount earned on Monday is $38 while $25 was earned on Tuesday.

The total amount earned for both days will be:

= $38 + $25

= $63

Since lucky bamboo plants are $7 each, we then divide the total amount gotten by $7. This will be:

= $63 / $7

= 9

Therefore, he can buy 9 lucky bamboos

7 0
2 years ago
charlie charted the rainfall in abilene over a one year period. what is the difference between the median and the mode of the da
sveticcg [70]
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3 years ago
Pls answer fast<br> (√3 + √11)² + (√3 - √11)²
Masja [62]

(√3 + √11)² + (√3 - √11)²

  • (a+b)² = a² + b² + 2ab
  • ( a - b )² = a² + b² - 2ab

<em>Now </em><em>,</em>

(√3 + √11)² + (√3 - √11)²

(3 + 11 + 2√3√11)+ (3 +11 - 2√3√11)

14 + 2√33+ 14 - 2√33

14 + 14 = 28

Hence , The value of (√3 + √11)² + (√3 - √11)² is 28 .

6 0
1 year ago
Read 2 more answers
A bag containing food has mass 3.813 kg. When the bag is empty its mass is 257 g. Find in kilograms the mass of the fruit
Elden [556K]

Answer:

I think it is 0.257 kg

Step-by-step explanation:

To change units from the gram to kilogram, you need to divide by 1000, because 1kg=1000g:

257÷1000= 0.257 Kg

5 0
2 years ago
5
Daniel [21]

Answer:

a,c,d

Step-by-step explanation:

8 0
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