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
padilas [110]
3 years ago
13

Prove that 1+cosA/sinA + sinA/1+cosA=2cosecA

Mathematics
1 answer:
Alla [95]3 years ago
5 0
\frac{1+cos\alpha}{sin\alpha}+\frac{sin\alpha}{1+cos\alpha}=2cosec\alpha\\\\L=\frac{(1+cos\alpha)(1+cos\alpha)+sin\alpha\cdot sin\alpha}{sin\alpha(1+cos\alpha)}=\frac{1+2cos\alpha+cos^2\alpha+sin^2\alpha}{sin\alpha(1+cos\alpha)}\\\\=\frac{1+2cos\alpha+1}{sin\alpha(1+cos\alpha)}=\frac{2+2cos\alpha}{sin\alpha(1+cos\alpha)}=\frac{2(1+cos\alpha)}{sin\alpha(1+cos\alpha)}\\\\=\frac{2}{sin\alpha}=2\cdot\frac{1}{sin\alpha}=2cosec\alpha=R
You might be interested in
2 u + 12 &lt; 23<br> 0,1 d + 8 &gt; 0<br> 3 - 4 r &gt; 7<br> 13 &lt; 2 z + 3<br> 6 ≥ 9 - 0, 15 i
BartSMP [9]

Answer:

Part 1) u< 5.5  

Part 2) d > -80

Part 3) r < -1

Part 4) z>5

Part 5) i\geq 20

Step-by-step explanation:

<u><em>The question is</em></u>

Solve each inequality for the indicated variable

Part 1) we have

2u+12

subtract 12 both sides

2u< 23-12\\2u

Divide by 2 both sides

u< 5.5

The solution is the interval (-∞,5.5)

In a number line the solution is the shaded area at left of u=5.5 (open circle)

The number 5.5 is not included in the solution

Part 2) we have

0.1d+8 >0

subtract 8 both sides

0.1d > -8

Divide by 0.1 both sides

d > -80

The solution is the interval (-80,∞)

In a number line the solution is the shaded area at right of d=-80 (open circle)

The number -80 is not included in the solution

Part 3) we have

3-4r> 7

Subtract 3 both sides

-4r>7-3\\-4r>4

Divide by -4 both sides

Remember that, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

r < -1

The solution is the interval (-∞,-1)

In a number line the solution is the shaded area at left of r=-1.1 (open circle)

The number -1.1 is not included in the solution

Part 4) we have

13< 2z+3

Subtract 3 both sides

13-3

Divide by 2 both sides

5

Rewrite

z>5

The solution is the interval (5,∞)

In a number line the solution is the shaded area at right of z=5 (open circle)

The number 5 is not included in the solution

Part 5) we have

6\geq 9-0.15i

Subtract 9 both sides

6-9\geq -0.15i\\-3\geq -0.15i

Divide by -0.15 both sides

Remember that, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

20\leq i

Rewrite

i\geq 20

The solution is the interval [20,∞)

In a number line the solution is the shaded area at right of i=20 (closed circle)

The number 20 is included in the solution

6 0
3 years ago
A sphere with a radius of 6cm has the same volume as a cylinder with a height of 4.5cm. What is the radius of the cylinder
yawa3891 [41]
Short answer: r = 8
Remark
The easiest way to do this is to solve the sphere's volume in terms of pi. When you do this, you can equate that to the formula for a cylinder and cancel the pi values. 

Step One
Find the volume of the sphere.

<em>Givens</em>
r = 6 cm

<em>Formula</em>
V = (4/3) pi r^3

<em>Sub and Solve</em>
V =  4/3 pi * 6^3
V = 288 * pi

Step two 
Find the radius of the cylinder

<em>Givens</em>
V = 288* pi cm^3
h = 4.5 cm

<em>Formula</em>
V = pi r^h

<em>Sub and solve</em>
288 pi cm^3 = pi r^2 * 4.5    Divide both sides by pi
288 cm^3 = 4.5 r^2              Divide both sides by 4.5
388 / 4.5 = r^2
64 = r^2                                Take the square root of both sides.
r = square root( 64)
r = 8 <<<<< Answer

4 0
2 years ago
14=2y/5 <br><br> What’s the answer
shutvik [7]
The answer is 35 ok ?
7 0
2 years ago
What is 900cm/h = cm/min? ( with an explanation not just the answer)
vladimir2022 [97]
I hope that helped :)

6 0
3 years ago
Find the equation of the plane that is parallel to the vectors left angle 3 comma 0 comma 3 right angle and left angle 0 comma 1
Sholpan [36]

Answer:

x + 3y -z - 3 = 0      

Step-by-step explanation:

We have to find the equation of plane that is parallel to the vectors

\langle 3,0,3\rangle, \langle0,1,3\rangle

The plane also passes through the point (2,0,-1).

Hence, the equation of plane s given by:

\displaystyle\left[\begin{array}{ccc}x-2&y-0&z+1\\3&0&3\\0&1&3\end{array}\right]\\\\=(x-2)(0-3) - (y-0)(9-0) + (z+1)(3-0)\\=-3(x-2)-9y+3(z+1)\\\Rightarrow -3x + 6 - 9y + 3z + 3 = 0\\\Rightarrow 3x + 9y -3z -9 = 0\\\Rightarrow x + 3y -z - 3 = 0

It is the required equation of plane.

4 0
3 years ago
Other questions:
  • Find the 12th term in the following geometric sequence. 0.75, 1.5, 3, 6, . . .
    5·2 answers
  • maria rolls a regular number cube with sides labeled 1 through 6 a total of 45 times. The number 4 is rolled 12 times. What is t
    10·1 answer
  • Explain how you know weather to add or subtract when you use the distributive property to multiply
    12·2 answers
  • PLZ ANSWER I CAN'T FAIL
    12·1 answer
  • Sally has 117 shares of stock valued at 2,614.95. Over the next three days, the value per share increases by $1.01,$0.11 and $0.
    7·1 answer
  • What is the range of the function shown in this table?
    8·1 answer
  • Write 21/23 as a decimal rounded to the nearest tenth.
    6·1 answer
  • The total population of Aiken County is 173,000 and there are approximately 23,000 students enrolled in Aiken County schools. Wh
    5·1 answer
  • Y'all can someone help me out with this? Pweassee? I really need it right now (ᗒᗣᗕ)՞
    6·1 answer
  • 7th grade math <br> (Look at photo!)<br> Easy math
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!