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
Nastasia [14]
3 years ago
10

Prove that 1+cosθ+sinθ/1+cosθ-sinθ = 1+sinθ/cosθ

Mathematics
1 answer:
marusya05 [52]3 years ago
3 0

Step-by-step explanation:

(1 + cos θ + sin θ) / (1 + cos θ − sin θ)

Multiply by the reciprocal:

(1 + cos θ + sin θ) / (1 + cos θ − sin θ) × (1 + cos θ + sin θ) / (1 + cos θ + sin θ)

(1 + cos θ + sin θ)² / [ (1 + cos θ − sin θ) (1 + cos θ + sin θ) ]

(1 + cos θ + sin θ)² / [ (1 + cos θ)² − sin² θ) ]

Distribute and simplify:

(1 + cos θ + sin θ)² / (1 + 2 cos θ + cos² θ − sin² θ)

[ 1 + 2 (cos θ + sin θ) + (cos θ + sin θ)² ] / (1 + 2 cos θ + cos² θ − sin² θ)

(1 + 2 cos θ + 2 sin θ + cos² θ + 2 sin θ cos θ + sin² θ) / (1 + 2 cos θ + cos² θ − sin² θ)

Use Pythagorean identity:

(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (sin² θ + cos² θ + 2 cos θ + cos² θ − sin² θ)

(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (2 cos² θ + 2 cos θ)

(1 + cos θ + sin θ + sin θ cos θ) / (cos² θ + cos θ)

Factor:

(1 + cos θ + sin θ (1 + cos θ)) / (cos θ (1 + cos θ))

(1 + cos θ)(1 + sin θ) / (cos θ (1 + cos θ))

(1 + sin θ) / cos θ

You might be interested in
A closed container has 3.06 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10–24 grams. Which of the following shows
Mars2501 [29]

Answer:

Step-by-step explanation:

The correct answer is not the first answer, but the second answer in the middle. The third answer is the correct one because, since it has the correct exponent, that is, 0.51 grams.

_________________________________________________________

The approximate total mass is the number of atoms multiplied by the weight of an atom.

The approximate overall mass=3.06 10²³ atoms. (1.67 10⁻²⁴ grams/1 atom) which is equivalent to a mass of 0.51 grams. (1.67 10⁻²⁴ grams/1 atom) = 0.51102 g ≈ 0.51 g

Answer: B. 0.51 grams, because (3.06 ⋅ 1.67) ⋅(1023 ⋅ 10–24) = 5.1102 ⋅ 10–1

5 0
3 years ago
Read 2 more answers
Please help extra points and Mark brainless
Naya [18.7K]
-1/6 Is the answer for this!!
4 0
3 years ago
If anyone could help me, it would be greatly appreciated!
Sav [38]

Answer: x=65^{\circ}, y=65^{\circ}, z=65^{\circ}

Step-by-step explanation:

All radii of a circle are congruent, so by the base angles theorem

  • z = y = (180-50)/2 = 65.

Also, angles x and y are inscribed in the same arc, and they are thus congruent, meaning x = 65.

7 0
2 years ago
A midwestern music competition awarded 38 ribbons. The number of blue ribbons awarded was 1 less than the number of white ribbon
Artist 52 [7]
Starting from what I know (the difference between ribbons), I decided to go from the bottom and work my way up. I then noticed a pattern (each sum was three more of the previous one), and decided to keep my pattern of the three numbers but not have to do any major mental work and instead add three to the previous sum until I got to 38.

4 0
3 years ago
A child wants to fill up a box with snow he can only carry the box if it weighs under 30 pounds the dimensions of the box are 30
Korolek [52]

Answer:

I thought that all races were = I thought it was fine we all loved each other and that there were protests. That the black lives matter. if a police officer kills a white man bc the white man is a threat then no one cares but if a police man kills a black man bc a black man is a threat everyone protests. I thought we were = but then black people are out there saying there lives matter. They do but white lives matter too so do blue lives and green lives and purple lives. Everyone matters but if you say that apparently you get in trouble. All lives matter but instead people had to make a program titled black lives matter.

Also guys you can love a guy as a friend just not in a gay way. That is not okay you are getting confused I love my friend who is the same gender as me but I don't get my feelings confused. Can yall just be straight please.

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • Please help!!will get brainliest!!
    12·1 answer
  • Which of the tables represents a function?
    10·2 answers
  • Find the original price if the sale price of the cell phone is $205.50 (discount is 30%)
    15·2 answers
  • G(t) = -(t - 1)2 +5<br> What is the average rate of change of g over the interval -4
    7·1 answer
  • Find x . round your answer to the nearest tenth of a degree
    13·2 answers
  • Answer to this question?
    10·2 answers
  • The diagram shows the field lines near the poles, X and Y, of two magnets.
    5·2 answers
  • I need answer please 6x + 3y + 2x + y
    9·2 answers
  • Solve the equation 5,4g+10=2.4g+25. a. Find the value of g. b. Explain how you can check that the value you found for g is corre
    14·2 answers
  • The radius of a circle is 4 feet. What is the circumference?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!