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
BartSMP [9]
3 years ago
12

Please please help!!

Mathematics
1 answer:
shepuryov [24]3 years ago
4 0

Answer:

\large\boxed{x=0\ and\ x=\pi}

Step-by-step explanation:

\tan^2x\sec^2x+2\sec^2x-\tan^2x=2\\\\\text{Use}\ \tan x=\dfrac{\sin x}{\cos x},\ \sec x=\dfrac{1}{\cos x}:\\\\\left(\dfrac{\sin x}{\cos x}\right)^2\left(\dfrac{1}{\cos x}\right)^2+2\left(\dfrac{1}{\cos x}\right)^2-\left(\dfrac{\sin x}{\cos x}\right)^2=2\\\\\left(\dfrac{\sin^2x}{\cos^2x}\right)\left(\dfrac{1}{\cos^2x}\right)+\dfrac{2}{\cos^2x}-\dfrac{\sin^2x}{\cos^2x}=2

\dfrac{\sin^2x}{(\cos^2x)^2}+\dfrac{2-\sin^2x}{\cos^2x}=2\\\\\text{Use}\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-(1-\cos^2x)}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-1+\cos^2x}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{1+\cos^2x}{\cos^2x}=2

\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{(1+\cos^2x)(\cos^2x)}{(\cos^2x)^2}=2\qquad\text{Use the distributive property}\\\\\dfrac{1-\cos^2x+\cos^2x+\cos^4x}{\cos^4x}=2\\\\\dfrac{1+\cos^4x}{\cos^4x}=2\qquad\text{multiply both sides by}\ \cos^4x\neq0\\\\1+\cos^4x=2\cos^4x\qquad\text{subtract}\ \cos^4x\ \text{from both sides}\\\\1=\cos^4x\iff \cos x=\pm\sqrt1\to\cos x=\pm1\\\\ x=k\pi\ for\ k\in\mathbb{Z}\\\\\text{On the interval}\ 0\leq x

You might be interested in
Can somebody tell me the answer to this ?
Dmitriy789 [7]

Answer:

16/93

Step-by-step explanation:

3 0
3 years ago
Custom Greetings places an order for 300 reams of card stock paper. Its supplier offers Custom Greetings a 35% trade discount. I
Y_Kistochka [10]

Answer:

<em>Net price: $4972.50</em>

Step-by-step explanation:

<u>Percentages</u>

We know a ream of paper has a list price of $25.50. Custom Greetings placed an order for 300 of them. If they have purchased them at list price, the total price would have been

300*25.50=$7,650

But we also know there was a 35% trade discount, so the net price of their order is

$7,650-$7,650*35/100=$4972.50

7 0
3 years ago
The product of two numbers​
sladkih [1.3K]

Answer:

The product of two numbers is the result you get when you multiply them together. So 12 is the product of 3 and 4, 0 is the product of 4 and 5 and so on.

Step-by-step explanation:

4 0
3 years ago
If 2k, 5k-1 and 6k+2 are the first 3 terms of an arithmetic sequence, find k and the 8th term​
Klio2033 [76]

Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = a_{2} - a_{1} = a_{3} - a_{2}

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

--------------------------------------------------------

The n th term of an arithmetic sequence is

a_{n} = a_{1} + (n - 1)d

a_{1} = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

a_{8} = 4 + (7 × 5) = 4 + 35 = 39

4 0
3 years ago
What is 3.42857142857 rounded to the nearest hundredth
Advocard [28]
3.43 look to the number to the right of the hundredths place. If it's higher than 5 round up.
7 0
3 years ago
Read 2 more answers
Other questions:
  • Mrs. Carlyle bought a bag of peanuts for her children. when Philip Joy Brent and Preston came home from school and they each too
    7·1 answer
  • please help me with this i asked last time but it didn’t some the important stuff so i’m just putting a picture ^
    8·1 answer
  • Using the Vertical Method to multiply these two polynomials, fill in the values for A, B, and C
    11·1 answer
  • Please please please please please please please please please please
    9·1 answer
  • What's the correct answer to this math problem?<br> 27.4-3.2×2
    14·2 answers
  • Write and solve an equation to find the value of x. PLS HELP!!
    7·2 answers
  • Anyone who know what the answer please please faster???!??!
    5·2 answers
  • Find the next term in the sequence. please type the number only as you answer. hint first figure out if the sequence is arithmet
    8·1 answer
  • 8÷7/9 (urgent) plzzz I need this​
    15·2 answers
  • PLEASE HELP!!!!!!!!!!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!!!!!!!!!!!!A moving-van rental company uses the polynomial 110 + 0.65(m
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!