![larrbear64](/avatars/25277.jpg)
larrbear64
30.09.2019 •
Mathematics
Which of the following is not an identity? a: (cosx+sinx)^2=1+2cosx sinx b: 1+cos^2x/sin^2=1 c: tan^2x=sec^2x-sin^2x-cos^2x d: (tanx+cotx)^2=csc^2x+sec^2x
Solved
Show answers
More tips
- F Food and Cooking How to Find Your Zip Code?...
- W Work and Career Can Skill Alone Make You a Professional?...
- C Computers and Internet How to Top Up Your Skype Account Without Losing Money?...
- P Philosophy Unidentified Flying Object - What is the Nature of this Phenomenon?...
- F Family and Home Protect Your Home or Apartment from Pesky Ants...
- O Other What is a Disk Emulsifier and How Does it Work?...
- F Family and Home What does a newborn need?...
- F Family and Home Choosing the Right Car Seat for Your Child: Tips and Recommendations...
- F Food and Cooking How to Get Reconfirmation of Registration?...
Answers on questions: Mathematics
- M Mathematics One number is four less than a second number. five times the first is 6 more than 6 times the second...
- M Mathematics Yang bought thrice as many blue marbles as pink marbles. he spent as much money on the blue marbles as he did on the pink marbkes. the difference between the cost of each blue marble...
- M Mathematics Calculate the distance between the two given point t(6,-2),u(-2,-12)...
- M Mathematics Ais an equation in the form a/b=c/d that states that two ratios are equal....
- M Mathematics Aman surveyed a sample of 36 high school students and asked, how many days in the past week have you consumed an alcoholic beverage? the results of the survey are shown to the right....
- M Mathematics Yy =6x−30 =x 2 −18x+114 if (a,b)(a,b)left parenthesis, a, comma, b, right parenthesis is the solution to the system of equations shown above, what is the value of bbb?...
- M Mathematics An olympic hurdler accelerates at a rate of 15.5 m/s2 . what is the rate in miles/min2 ? 1. 6.89 miles/min2 2. 31.8 miles/min2 3. 2.69 miles/min2 4. 1.15 miles/min2 5. 34.7 miles/min2...
- M Mathematics Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify (6x^-2)^2(.5x)^4 show work...
- M Mathematics | 8x−2 | 6 | 5x−8 | ≥ 3 | x−2 | ≥ 6 | x+7 | ≥ −2 | 2x−6 | ≤ −6 | x+16/8 | 3...
- M Mathematics A__is marked by two sets of double yellow lines with each set having a broken line on the outside...
Ответ:
(cosx+sinx)² = 1 + 2cosxsinx
Foil the left side.
cos²x + 2cosxsinx + sin²x = 1 + 2cosxsinx
Subtract 2cosxsinx from each side.
cos²x + sin²x = 1
And we're left with the Pythagorean identity!
Looks like it's not A.
Part B
( 1 + cos²x ) / sin²x = 1
Multiply each side by sin²x.
1 + cos²x = sin²x
Immediately, you should see a problem with this, and here's why:
Our Pythagorean identity from earlier can be put like this:
sin²x = 1 - cos²x
Substitute 1 - cos²x for sin²x in our earlier equation, and you get
1 + cos²x = 1 - cos²x
Which is clearly incorrect!
(If you really needed to verify this...subtract 1, divide by cos²x to get 1 = -1)
B is not an identity.
Part C
tan²x = sec²x - sin²x - cos²x
You might be able to recognize something from our Pythagorean identity.
Factor out a -1 from -sin²x - cos²x...
tan²x = sec²x -1(sin²x + cos²x)
Using our Pythagorean identity, 1 = sin²x + cos²x...
tan²x = sec²x - 1
Hey, look! Another trig identity! Don't recognize it? here...
sin²x/cos²x = 1/cos²x - 1
Multiply by cos²x...
sin²x = 1 - cos²x
There's also a great diagram for remembering the basic trig identities (besides double angle, half angle, angle addition and subtraction) called the magic hexagon...look it up, it's a great tool!
Part D
(tanx+cotx)² = csc²x + sec²x
This one sucks to prove but we can always use our last resort: expressing in terms of sine and cosine.
(sinx/cosx + cosx/sinx)² = (1/sinx)² + (1/cosx)²
Get the fractions on the left into a common denominator sinxcosx.
(sin²x/sinxcosx + cos²x/sinxcosx)² = (1/sinx)² + (1/cosx)²
(sin²x+cos²x/sinxcosx)² = (1/sinx)² + (1/cosx)²
(1/sinxcosx)² = (1/sinx)² + (1/cosx)²
Get the fractions on the right into a common denominator.
(1/sinxcosx)² = 1/sin²x + 1/cos²x
(1/sinxcosx)² = cos²x/sin²xcos²x + sin²x/sin²xcos²x
(1/sinxcosx)² = (sin²x+cos²x)/sin²xcos²x
(1/sinxcosx)² = 1/sin²xcos²x
(1/sinxcosx)² = (1/sinxcosx)²
Ответ: