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
shtirl [24]
2 years ago
10

Prove it :

Mathematics
1 answer:
solmaris [256]2 years ago
5 0

Heya!

\text{First, manipulate the left side.}\\\text{Use the rule:}~a-b=\frac{(a-b)(a-b)}{a+b} = \frac{a^2-b^2}{a+b} \\\text{Use the identity:}~1-sin^2(x)=cos^2(x)\\\frac{1+cos(x)-sin(x)}{1+cos(x)+sin(x)}  = \frac{cos(x)+\frac{cos^2(x)}{1+sin(y)}}{1+cos(x)+sin(x)}

\text{Second, simplify the numerator}~cos(x)+\frac{cos^2(x)}{1+sin(x)}\\\text{Convert element to a fraction:}~cos(x)=\frac{cos(x)(1+sin(x))}{1+sin(x)}\\\text{Add:}~cos(x)=\frac{cos(x)(1+sin(x))}{1+sin(x)}+\frac{cos^2(x)}{1+sin(x)}\\\text{The denominators are equal so combine:}~\frac{cos(x)(1+sin(x))+cos^2(x)}{1+sin(x)}\\\text{Simplify:} \frac{\frac{cos(x)(sin(x)+1)+cos^2(x)}{1+sin(x)} }{1+cos(x)+sin(x)}\\ \text{Apply fraction rule:}~\frac{cos(x)(1+sin(x))+cos^2(x)}{1+sin(x)}\\\\

\text{Factor:}~\frac{cos(x)(1+sin(x)+cos(x))}{(1+sin(x))(1+cos(x)+sin(x))} \\\text{Simplify:}~\frac{cos(x)}{1+sin(x)}

\text{Third, manipulate the right side.}\\\text{Use the basic trigonometric identity:}~sec(x)=\frac{1}{cos(x)} \\\text{Use the basic trigonometric identity:}~tan(x)=\frac{sin(x)}{cos(x)} \\\text{Put the expression back together:}~\frac{1}{cos(x)}-\frac{sin(x)}{cos(x)}\\\text{Simplify:}~\frac{\frac{cos^2(x)}{1+sin(x)} }{cos(x)}

\text{Fourth, simplify.}\\\text{Apply the fraction rule:}~\frac{cos^2(x)}{(1+sin(x))cos(x)} \\\text{Cancel out the common factor:}~\frac{cos(x)}{1+sin(x)}

Therefore, the expression is TRUE.

Best of Luck!

You might be interested in
Which is a true statement about the diagram?
Cloud [144]

<em>The </em><em>right</em><em> answer</em><em> is</em><em> </em><em>of </em><em>option </em><em>C.</em>

<em>hope </em><em>it </em><em>helps.</em><em>.</em>

<em>good </em><em>luck</em><em> on</em><em> your</em><em> assignment</em>

8 0
2 years ago
Carlota has 3/4 ton of mulch she is going to divide evenly among 5 flower beds. How much mulch will each flower bed contain? Ple
Murljashka [212]
The first thing to do is to turn 5 into a fraction.  
5 = 5/1

Now it is just a simple fractional division question: 
3/4 / 5/1

With fractional division, all you do is switch around the fraction that is on the right and turn the divide sign into a multiplication sign: 
3/4 X 1/5

Now you simply multiply the numerators together, and the denominators together: 
3 X 1 = 3
4 X 5 = 20

3/20. 

Each flower bed will contain 3/20 of a ton of mulch. 

5 0
2 years ago
Ms. Johnson was taking measurements in the Arctic Ocean and measured a temperature of -14.4 degrees Celsius. The temperature inc
otez555 [7]

Answer:

qwertyuiop

Step-by-step explanation:

3 0
2 years ago
Willing to give brainlyest if you can aswer these for me ASAP<br>​
vichka [17]

Answer:

65

Step-by-step explanation:

its simple math

5 0
2 years ago
Read 2 more answers
K-1234=5678<br> what does k equal
artcher [175]

Answer:

k=6,912

Step-by-step explanation:

5678+1234=6912

5 0
3 years ago
Read 2 more answers
Other questions:
  • a diagonal shortcut across an empty rectangular lot is 97 feet . the lot is 72 feet long , what is the other dimension of the lo
    7·1 answer
  • What is the best estimate for the sum if 3/8 and 1/12
    9·1 answer
  • PLEAZEE HELP ME??.....
    12·1 answer
  • The function h(x) = –x5 + 12x is an odd function. Which transformation of h(x) results in an odd function? A.h(5 – x) B.1 + h(x)
    8·2 answers
  • Solving Equations. 2(a-3)=5a+3a
    8·2 answers
  • What are the possible degrees for the polynomial function
    15·2 answers
  • Plz hurry brainleist and 17 or 18 points garranteed
    10·2 answers
  • Plz help due tomorrow
    11·2 answers
  • An equilateral triangle with side length 9 cm is shown in the diagram, work out the area of the triangle.
    10·1 answer
  • solve each triangle described below round measures of sides to the nearest tenth and angles to the nearest degree a=14 c=20 b=38
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!