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
nadezda [96]
3 years ago
8

1. cot x sec4x = cot x + 2 tan x + tan3x

Mathematics
1 answer:
Mars2501 [29]3 years ago
5 0
1. cot(x)sec⁴(x) = cot(x) + 2tan(x) + tan(3x)
    cot(x)sec⁴(x)            cot(x)sec⁴(x)
                   0 = cos⁴(x) + 2cos⁴(x)tan²(x) - cos⁴(x)tan⁴(x)
                   0 = cos⁴(x)[1] + cos⁴(x)[2tan²(x)] + cos⁴(x)[tan⁴(x)]
                   0 = cos⁴(x)[1 + 2tan²(x) + tan⁴(x)]
                   0 = cos⁴(x)[1 + tan²(x) + tan²(x) + tan⁴(4)]
                   0 = cos⁴(x)[1(1) + 1(tan²(x)) + tan²(x)(1) + tan²(x)(tan²(x)]
                   0 = cos⁴(x)[1(1 + tan²(x)) + tan²(x)(1 + tan²(x))]
                   0 = cos⁴(x)(1 + tan²(x))(1 + tan²(x))
                   0 = cos⁴(x)(1 + tan²(x))²
                   0 = cos⁴(x)        or         0 = (1 + tan²(x))²
                ⁴√0 = ⁴√cos⁴(x)      or      √0 = (√1 + tan²(x))²
                   0 = cos(x)         or         0 = 1 + tan²(x)
         cos⁻¹(0) = cos⁻¹(cos(x))    or   -1 = tan²(x)
                 90 = x           or            √-1 = √tan²(x)
                                                         i = tan(x)
                                                      (No Solution)

2. sin(x)[tan(x)cos(x) - cot(x)cos(x)] = 1 - 2cos²(x)
              sin(x)[sin(x) - cos(x)cot(x)] = 1 - cos²(x) - cos²(x)
   sin(x)[sin(x)] - sin(x)[cos(x)cot(x)] = sin²(x) - cos²(x)
                               sin²(x) - cos²(x) = sin²(x) - cos²(x)
                                         + cos²(x)              + cos²(x)
                                             sin²(x) = sin²(x)
                                           - sin²(x)  - sin²(x)
                                                     0 = 0

3. 1 + sec²(x)sin²(x) = sec²(x)
           sec²(x)             sec²(x)
      cos²(x) + sin²(x) = 1
                    cos²(x) = 1 - sin²(x)
                  √cos²(x) = √(1 - sin²(x))
                     cos(x) = √(1 - sin²(x))
               cos⁻¹(cos(x)) = cos⁻¹(√1 - sin²(x))
                                 x = 0

4. -tan²(x) + sec²(x) = 1
               -1               -1
      tan²(x) - sec²(x) = -1
                    tan²(x) = -1 + sec²
                  √tan²(x) = √(-1 + sec²(x))
                     tan(x) = √(-1 + sec²(x))
            tan⁻¹(tan(x)) = tan⁻¹(√(-1 + sec²(x))
                             x = 0
You might be interested in
Given a dilation around the origin, what is the scale factor K?<br><br> D o, K = (2,4) → (3,6)
fenix001 [56]

Answer: 3/2

Step-by-step explanation:

5 0
3 years ago
Perímetro de un cubo de 9 cm​
svp [43]

Answer:

Perímetro de

Step-by-step explanation:

What does this mean?

5 0
3 years ago
What two numbers multiply to give you -64 and add up to 0?
aksik [14]
I think it’s Positive 5
7 0
2 years ago
Read 2 more answers
One and read or both rode bicycles from the park to Main Street the graphs below represent the time and distance for each studen
Harman [31]
Juan did.

The line on his graph takes longer to get to 8 blocks.;-D


7 0
3 years ago
Select all of the following that are quadratic equations.
taurus [48]
A,d,f!!!!!!++!!!+!!!!!!
4 0
3 years ago
Read 2 more answers
Other questions:
  • Slope intercept form 2x-3y=12
    12·2 answers
  • Is 419108 divisible by 4?
    10·2 answers
  • Math question:<br> Solve for x<br> 2/3(x - 7) = -2
    11·1 answer
  • What is the slope of the line that passes through (2,3) and (6, - 4)?
    11·1 answer
  • Two marbles are randomly drawn from a bag containing 3 purple, 1 blue, and 1 yellow marble. The first marble is blue and is not
    6·1 answer
  • Solve 7x/3&lt;2<br> {X I X&lt;6/7}<br> {X I X&gt;6/7}<br> {X I X&lt;-14/3}<br> {X I X&gt;-14/3}
    13·1 answer
  • What is the answer to 4 and 5?
    11·1 answer
  • Solve the questions ​
    10·1 answer
  • 12x3-3x2=0 solve the equation by factoring
    11·1 answer
  • How long is the arc intersected by a central angle of startfraction pi over 3 endfraction radians in a circle with a radius of 6
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!