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
Veronika [31]
3 years ago
8

Please help if you can. I will give Brainiest to best answer. This question is a Calculus/Trigonometry question. I ask that you

look over my work, but if you don't have the time, I ask that you help me answer the questions I don't know.

Mathematics
1 answer:
Ierofanga [76]3 years ago
3 0

7 is incorrect. The answer should be -4. Here's how I'd derive it:

\tan^2\dfrac x2=\dfrac{\sin^2\frac x2}{\cos^2\frac x2}=\dfrac{\frac{1-\cos x}2}{\frac{1+\cos x}2}=\dfrac{1-\cos x}{1+\cos x}

With \pi, we should expect \cos x. If \tan x=\dfrac8{15}, then

\sec x=-\sqrt{1+\tan^2x}=-\dfrac{17}{15}\implies\cos x=-\dfrac{15}{17}

Also,

\pi

so we should expect \tan\dfrac x2 and

\tan\dfrac x2=-\sqrt{\dfrac{1-\cos x}{1+\cos x}}=-4

You seem to be taking

\tan\dfrac x2=\dfrac{1+\cos x}{-\sin x}

but this is not an identity.

###

8 is incorrect. Just a silly mistake, you swapped the order of the terms in the numerator. It should be

\dfrac{\sqrt6-\sqrt2}4

###

9. Use the identity from (7). \dfrac{7\pi}{12} lies in the second quadrant, so

\tan\dfrac{7\pi}{12}=-\sqrt{\dfrac{1-\cos\frac{7\pi}6}{1+\cos\frac{7\pi}6}}=-\sqrt{7+4\sqrt3}=-2-\sqrt3

###

12.

\dfrac{\cot x-1}{1-\tan x}=\dfrac{\frac{\cos x}{\sin x}-1}{1-\frac{\sin x}{\cos x}}

=\dfrac{\cos x(\cos x-\sin x)}{\sin x(\cos x-\sin x)}

=\dfrac{\cos x}{\sin x}

=\dfrac{\csc x}{\sec x}

###

13.

\dfrac{1+\tan x}{\sin x+\cos x}=\dfrac{1+\frac{\sin x}{\cos x}}{\sin x+\cos x}

=\dfrac{\cos x+\sin x}{\cos x(\sin x+\cos x)}

=\dfrac1{\cos x}

=\sec x

###

14.

\sin2x(\cot x+\tan x)=2\sin x\cos x\left(\dfrac{\cos x}{\sin x}+\dfrac{\sin x}{\cos x}\right)

=2\sin x\cos x\dfrac{\cos^2x+\sin^2x}{\sin x\cos x}

=2

###

15.

\dfrac{1-\tan^2\theta}{1+\tan^2\theta}=\dfrac{1-\frac{\sin^2\theta}{\cos^2\theta}}{1+\frac{\sin^2\theta}{\cos^2\theta}}

=\dfrac{\cos^2\theta-\sin^2\theta}{\cos^2\theta+\sin^2\theta}

=\cos2\theta

You might be interested in
Solve for x x -8 = -14
Anit [1.1K]

Answer:

-6

Step-by-step explanation:

x - 8 = -14

Add 8 to both sides of the equation

x - 8 + 8 = -14 + 8

x = -6

4 0
3 years ago
Read 2 more answers
Find the mean of the data in the pictograph below.
strojnjashka [21]
The answer is 12. Ann's
8 0
3 years ago
Read 2 more answers
A rectangular prism has a length of 20 in., a width of 2 in., and a height of 3 1/4 in. The prism is filled with cubes that have
STALIN [3.7K]
5,400 cubes is needed to fill the rectangular prism.
3 0
3 years ago
How do I distinguish between and use both part-to-part and part-to_whole ratios in comparisons?
HACTEHA [7]
An example of a part to a whole ratio is the number of females in a class to the number of students in the class. If there are 8 females in the class of 20 students the ratio of girls to students can be expressed 8:20 (females to students). Because this ratio is relating a part to a whole it can also be expressed as a fraction (8/20) or as a percentage (40%).
5 0
3 years ago
What is 82% as a decimal
Alik [6]
82% to decimal is 0.82
7 0
3 years ago
Read 2 more answers
Other questions:
  • (WILL MARK AS BRAINLIEST) Consider the graph of quadrilateral WXYZ.
    10·2 answers
  • PLEASE HELP!!!!!<br> What is the unit rate for 644.8 ft in 31 s? Enter your answer as a decimal.
    8·2 answers
  • The formula F(C) = 9/5 C + 32 calculates the temperature in degrees Fahrenheit, given a temperature in degrees Celsius.
    13·2 answers
  • Solve for x 3x+3-x+(-7)&gt;6
    12·1 answer
  • PLEASE HURRY!! The ratio of the volumes of two geometrically similar pyramids is 1 : 8. If the height of the larger pyramid is 2
    14·2 answers
  • Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arr
    6·1 answer
  • Solve w substitution please
    9·1 answer
  • A principal randomly chose 40 students from grade 7. Of these students, 9 were wearing watches. Based on this information, what
    5·1 answer
  • If the diameter is 6 feet what is the circumference in feet
    13·1 answer
  • thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!