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
Juliette [100K]
3 years ago
13

Simplify tan squared times (1 + cot squared x)

Mathematics
2 answers:
KonstantinChe [14]3 years ago
8 0

\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1 \\\\ 1+cot^2(\theta)=csc^2(\theta) \\\\ 1+tan^2(\theta)=sec^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ tan^2(x)[1+cot^2(x)]\implies tan^2(x)[csc^2(x)]\implies \cfrac{\underline{sin^2(x)}}{cos^2(x)}\cdot \cfrac{1}{\underline{sin^2(x)}} \\\\\\ \cfrac{1}{cos^2(x)}\implies sec^2(x)

cricket20 [7]3 years ago
6 0

\tan^2x\cdot(1+\cot^2x)\\\\\text{use}\ \tan x=\dfrac{\sin x}{\cos x}\ \text{and}\ \cot x=\dfrac{\cos x}{\sin x}\\\\=\left(\dfrac{\sin x}{\cos x}\right)^2\cdot\left[1+\left(\dfrac{\cos x}{\sin x}\right)^2\right]\\\\\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\dfrac{\sin^2x}{\cos^2x}\cdot\left(1+\dfrac{\cos^2x}{\sin^2x}\right)\\\\\text{use distributive property}\\\\=\dfrac{\sin^2x}{\cos^2x}\cdot1+\dfrac{\sin^2x}{\cos^2x}\cdot\dfrac{\cos^2x}{\sin^2x}

=\dfrac{\sin^2x}{\cos^2x}+1=\left(\dfrac{\sin x}{\cos x}\right)^2+1=\tan^2x+1\\\\or\\\\=\dfrac{\sin^2x}{\cos^2x}+1=\dfrac{\sin^2x}{\cos^2x}+\dfrac{\cos^2x}{\cos^2x}=\dfrac{\sin^2x+\cos^2x}{\cos^2x}\\\\\text{use}\ \sin^2x+\cos^2x=1\\\\=\dfrac{1}{\cos^2x}=\left(\dfrac{1}{\cos x}\right)^2\\\\\text{use}\ \sec x=\dfrac{1}{\cos x}\\\\=\sec^2x\\\\Answer:\ \tan^2x+1=\dfrac{1}{\cos^2x}=\sec^2x

You might be interested in
Ray bought 5 lemons and 3 limes for $7.20. Lia bought 4 lemons and 6 limes for the same price. How much would it cost to buy 1 l
kolezko [41]

Answer:

$1.60

Step-by-step explanation:

Please see the attached pictures for full solution.

5 0
3 years ago
Find the length of the side of a square, given that the area of the square minus the length of a side is 812.
Vlad [161]

Answer:

28.5

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
63.92 divided by 4.7
FinnZ [79.3K]

The answer would be 13.6

7 0
3 years ago
What is the volume of the composite figure?
saw5 [17]

volume of a sphere is 4/3 * PI * r^3

r = 6

r^3 = 6^3 = 216

4/3 * 216 = 288

 Volume = 288 PI in^3

3 0
3 years ago
1. In the figure, m DE=124, and M BC=36. The diagram is not drawn to scale. What is m A? A) 44* B) 62* C) 80* D) 88* please help
Anuta_ua [19.1K]

The relation between arc length and exterior angle is given in the figure.

Now we are given far arc length as DE =124

We are given near arc length as BC = 36

So plugging in the formula to find measure of angle A:

angle A=\frac{far arc-near arc}{2}

angle A=\frac{124-36}{2}

angle A=\frac{88}{2}

Angle A = 44 degrees

Answer : A) 44 degree


5 0
3 years ago
Read 2 more answers
Other questions:
  • How much of each ingredient would you need to make an identical recipe that serves 18 people? Explain your reasoning
    10·1 answer
  • Solve. −4.2y+2.1>−2.52 Drag and drop a number or symbol into each box to show the solution. <>0.11.14.62−4.62 y
    9·2 answers
  • Can anyone please help me with this question 61
    9·1 answer
  • 115 On a coordinate plane, draw triangle ABC with vertices
    9·1 answer
  • Factor 8x+16y+44 i offered up 15 points
    7·2 answers
  • How do you graph f(x)=-0.5+2, x<2
    9·1 answer
  • Nico rolled two numbers 250 times
    15·1 answer
  • What is the value of the 20th term in this sequence? f(n)=6n−18
    11·1 answer
  • Ok guys i have only 1 hr to get this. Determine the y-intercept for the equation 3x + 2y = 12. HELP
    15·1 answer
  • A) side angle side<br> b) side side side <br> c) angle side angle<br> d) not congruent
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!