1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ZanzabumX [31]
3 years ago
14

Write the expression as either the sine, cosine, or tangent of a single angle. tan5x - tan2y / 1 + tan5x tan2y

Mathematics
1 answer:
Kryger [21]3 years ago
6 0
\bf \textit{Sum and Difference Identities}
\\\\
tan(\alpha + \beta) = \cfrac{tan(\alpha)+ tan(\beta)}{1- tan(\alpha)tan(\beta)}
\qquad
tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)}\\\\
-------------------------------\\\\
\cfrac{tan(5x)-tan(2y)}{1+tan(5x)tan(2y)}\implies tan(5x-2y)
You might be interested in
If you could show as much work as possible that would be amazing!!
Nikitich [7]

Answers:

<u>Reduce:</u>

Here we gave to simplify the expressions:

9) x^{2}+7x+\frac{12}{x^{2}}+11x+28

Grouping similar terms:

(x^{2}+\frac{12}{x^{2}})+(18x+28)

Applying common factor x^{2} in the first parenthesis and common factor 2 in the second parenthesis:

x^{2}(1+\frac{12}{x^{4}})+2(9x+14) This is the answer

11) y^{3}+\frac{27}{y^{2}}+2y-3

Rearranging the terms:

(y^{3}+2y)+(\frac{27}{y^{2}}-3)

Applying common factor y in the first parenthesis and common factor 3 in the second parenthesis:

y(y^{2}+2)+3(\frac{9}{y^{2}}-1) This is the answer

<u>Multiply:</u>

19) (\frac{12a^{9}u^{7}}{15 c})(\frac{3c^{4}}{21a^{13 u^{8}}})

Multiplying both fractions:

\frac{36 a^{9}u^{7}c^{4}}{315 c a^{13}u^{8}}

Dividing numerator and denominator by 3 and simplifying:

\frac{12 c^{3}}{105 c a^{4}u} This is the answer

21) (x-\frac{3}{x}-7)(x^{2}-9x+\frac{35}{x^{2}}-18)

(\frac{x^{2}-3-7x}{x})(\frac{x^{4}-9x^{3}+35-18x^{2}}{x^{2}})

Operating with cross product:

x^{2} (x^{2}-3-7x) x(x^{4}-9x^{3}+35-18x^{2})

x^{9} -9x^{8} -18x^{7}+35x^{5}-7x^{8}  +63x^{7}+126x^{6}-245x^{4}-3x^{7}+27x^{6}+54x^{5}-105x^{3}

Grouping similar terms and factoring:

x^{9}-2(8x^{8}+21x^{7} )+153x^{6}+89x^{5}-5(49x^{4}+21x^{3}) This is the answer

<u>Divide:</u>

29) \frac{\frac{k^{6}}{x^{2}}}{\frac{2k^{4}}{3x^{6}}}

\frac{3k^{6}x^{6}}{2x^{2}k^{4}}

Simplifying:

\frac{3}{2} k^{2}x^{4} This is the answer

33) \frac{\frac{x+5}{x+1}}{\frac{x^{2}+11x+30}{x^{2}+3x+2}}

\frac{(x+5)(x^{2}+3x+2)}{(x+1)(x^{2}+11x+30)}

Factoring numerator and denominator:

\frac{(x+5)(x+2)(x+1)}{(x+1)(x+6)(x+5)}

Simplifying:

\frac{x+2}{x+6} This is the answer

37) \frac{\frac{x-10}{x+13}}{\frac{x^{3}-1000}{x^{2}+15x+21}}

\frac{(x-10)(x^{2}+15x+21)}{(x+13)(x^{3}-1000)}

Applying the distributive property in numerator and denominator:

\frac{x^{3}+15x^{2}+21x-10x^{2}-150x-210}{(x+13)(x^{4}-1000x+13x^{3}-13000)}

Grouping similar terms and factoring by common factor:

-\frac{5x(x^{2}-129)(x^{2}-42)}{1000x^{3} (x+13)(x-13)}

Dividing by 5 in numerator and denominator and simplifying:

-\frac{(x^{2}-129)(x^{2}-42)}{200x^{2}(x+13)(x-13)} This is the answer

3 0
3 years ago
Use the rulers to help you estimate the perimeter of this triangle. <br> 6.5 in. 3 in. 6 in. 7 in.
777dan777 [17]

Answer:

6 inches

Step-by-step explanation:

The perimeter of a triangle is a + b + c

Where, a, b, c are the length of the 3 sides of the triangle ;

Using the ruler ;

a = 1.5

b = 2

c = 2.5

Therefore,

a + b + c

1.5 + 2 + 2.5

= 6 in

6 0
3 years ago
Read 2 more answers
Add the following decimals​
Fantom [35]

Answer:

148.91

Step-by-step explanation:

hope it helps<333

5 0
3 years ago
Notebooks are originally on sale for $2.00. This school year they were marked up by 15%. What's
Aleks04 [339]

Answer:

the new notebook price is

Step-by-step explanation:

10% of $2.00 is 20 cents. 5% is 10 cents. 20+10= 30. 30 cents. $2.00+30 = $2.30

5 0
3 years ago
Could someone answer these 3 questions?h
Aleks04 [339]
9) x= -6
10) x= 3/2
11) x= -4,0,5
12) no solution
8 0
3 years ago
Other questions:
  • Melinda ate breakfast and wanted to leave her waitress a 20% tip her meal cost $7.50 How much money should Melinda leave for the
    13·2 answers
  • In how many ways can 3 letters out of five distinct 5 distinct letters A, B, C, D and E be arranged in a straight line so that A
    12·1 answer
  • Linda had a garage sale
    15·1 answer
  • CAN SOMEONE HELP ME WITH THIS QUESTION???? I NEED HELP QUICK!!!!!!!!!
    13·1 answer
  • Find the value of the following expression:
    8·2 answers
  • 3(2x-4)-5(x+3)2<br> Which expression is the simplest form of<br> 3
    8·1 answer
  • Please help quickly!!<br> What is the radius, diameter and r2 of a circle with a 3cm area?
    14·1 answer
  • Which equation shows the vertex form of a quadratic equation with vertex (2, 5)?
    14·1 answer
  • If the surface area of a sphere is 48.3cm^2, find its diameter. PLEASE HURRY
    5·1 answer
  • HELP!! LOOK AT THE PIC AND SOLVE IT. <br> HELP WILL BE APPRECIATED
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!