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
BabaBlast [244]
3 years ago
10

Can someone please explain this problem step by step? Thank you sooooooooooooo much!

Mathematics
1 answer:
love history [14]3 years ago
7 0

Explanation:

Use the Pythagorean identity, cancel common factors, and divide numerator and denominator by cos(x). Equivalently, multiply numerator and denominator by sec(x).

\dfrac{\sin^2{x}+2\cos{x}-1}{\sin^2{x}+3\cos{x}-3}=\dfrac{1-\cos^2{x}+2\cos{x}-1}{1-\cos^2{x}+3\cos{x}-3} \qquad\text{replace $\sin^2$ with $1-\cos^2$}\\\\=\dfrac{\cos{x}(2-\cos{x})}{(\cos{x}-1)(2-\cos{x})}=\dfrac{\cos{x}}{\cos{x}-1}=\dfrac{1}{\dfrac{\cos{x}}{\cos{x}}-\dfrac{1}{\cos{x}}}=\dfrac{1}{1-\sec{x}}

You might be interested in
Determine whether each expression can be used to find the length of side AB. Match Yes or No for each
tankabanditka [31]

Answer:

(a)\ AB = \frac{7}{\sin (B)}  \to Yes

(b)\ AB = \frac{24}{\cos (B)} \to Yes

(c)\ AB = \frac{24}{\cos (A)} \to No

(d)\ AB = \frac{7}{\cos (A)}  \to Yes

Step-by-step explanation:

Given

BC =24

AC = 7

Required

Select Yes or No for the given options

(a)\ AB = \frac{7}{\sin (B)}  \to Yes

Considering the sine of angle B, we have:

\sin(B) = \frac{Opposite}{Hypotenuse}

\sin(B) = \frac{7}{AB}

Make AB, the subject

AB = \frac{7}{\sin(B)}

(b)\ AB = \frac{24}{\cos (B)} \to Yes

Considering the cosine of angle B, we have:

\cos(B) = \frac{Adjacent}{Hypotenuse}

\cos(B) = \frac{24}{AB}

Make AB the subject

AB = \frac{24}{\cos(B)}

(c)\ AB = \frac{24}{\cos (A)} \to No

Considering the cosine of angle B, we have:

\cos(A) = \frac{Adjacent}{Hypotenuse}

\cos(A) = \frac{7}{AB}

Make AB the subject

AB = \frac{7}{\cos(A)}

(d)\ AB = \frac{7}{\cos (A)}  \to Yes

<em>This has been shown in (c) above</em>

3 0
3 years ago
2 2/3 divides by 1 3/5
Anarel [89]
1 2/3 . Hope this helps ;)
8 0
3 years ago
Read 2 more answers
Write the equation in slope intercept form given the following
zvonat [6]

Answer:

the first answer is: y=2x  the second answer is y=2x+10

Step-by-step explanation:

6 0
3 years ago
A circle has a circumference of 18. It has an arc of 6. What is the central angle of the arc, in degrees?
irga5000 [103]

Answer:

Step-by-step explanation:

C=2πr

18=2×3.14×r

18=6.28r

r=2.88

Arc of a circle

A=®/360°πr

6=®/360°×3.14×r

®=239°

6

3 0
3 years ago
Read 2 more answers
12. A flat, square roof needs a square patch in the corner to seal a leak. The side length of
NISA [10]

Answer:

Step-by-step explanation:

Area of the good part= area of whole roof - area of bad part

Since the roof is a square roof, the area will be calculated using the formulae for area of a square

Area of a square =length²

Area of good part =(x+12)²-x²

A= {(x+12)(x+12)} - x²

A = (x²+12x+12x+144) -x²

Open the bracket and rearrange the equation

A= x²-x²+24x+144

A=(24x+144) ft

5 0
3 years ago
Other questions:
  • Can you please help me
    13·1 answer
  • Only the correct answer please
    6·2 answers
  • the student to faculty ratio at a small college is 17:3. the total of students and faculty is 740. how many faculty members are
    10·2 answers
  • Does anyone know the answer to this? I’m stumped
    9·1 answer
  • Last question on this site if anyone wanna help
    10·1 answer
  • F(x) = log10 (x) + 5
    11·1 answer
  • YO please help actually been waiting for an hour and a half cuz so many trolls lol. &lt;3 giivng brainliest, and ty in advance g
    15·2 answers
  • The new Samsung 9 phone costs $500, and has a sales tax of 15%. What is the final price?
    13·1 answer
  • WILL MARK BRAINLIEST IF GOTTTEN RIGHT
    12·1 answer
  • Michael Chan leaves a dock in his motorboat and travels at an average speed of 9 mph toward the Isle of Shoals, a small island o
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!