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2 years ago

Prove that . 1+cot2 theta = cosec2theta

Mathematics

1 answer:

igor_vitrenko [27]2 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

Using the Pythagorean identity

sin²θ + cos²θ = 1 ( divide terms by sin²θ )

$\frac{sin^20}{sin^20}$ + $\frac{cos^20}{sin^20}$ = $\frac{1}{sin^20}$ , that is

1 + cot²θ = cosec²θ ← as required

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kirill115 [55]

Answer:

$\frac{4}{3}$ hrs/house

Step-by-step explanation:

Rate is the amount of work done per unit of time;

Let Cara's rate = C

Let Jena's rate = J

C + J = 4 ------ i

Now;

Working alone:

Jena takes twice as long as Cara

J = 2C ---- i

How long does it take Cara to clean a house alone

C + J = 4

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C + 2C = 4

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C = $\frac{4}{3}$ hrs/house

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2 years ago

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3 years ago

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Choose the graph below that has an undefined slope.

Ronch [10]

Answer:

The correct option is A.

Step-by-step explanation:

The first line passing through the points (-6,2) and (-6,0).

The slope of a line is

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The slope of first line is

$m_1=\frac{0-2}{-6-(-6)}=\infty$

The second line passing through the points (0,-4) and (-1,1). The slope of second line is

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The third line passing through the points (0,-6) and (2,-6). The slope of third line is

$m_3=\frac{-6-(-6)}{2-0}=0$

The fourth line passing through the points (0,6) and (-3,-7). The slope of fourth line is

$m_4=\frac{-7-6}{-3-0}=\frac{13}{3}$

Since the slope of a vertical line is infinity, Therefore option A is correct.

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2 years ago

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Emma is taking out a loan in the amount of $25,000. Her choices for the loan are a 60-month loan at 5% annual simple interest an

My name is Ann [436]

Answer:

The answer is $2750. Which is the difference in the amount of interest Emma would have to pay for these two loans

Step-by-step explanation:

Interest=( P× r × t)/100

60 months is converted to 5years(60/12=5)

Interest= (25000 × 5 × 5) /100

= $6250

72months is converted to 6 years(72/12=6 Years)

Interest=( P× r × t)/100

= (25000 × 6 × 6)/100

=$ 9000

The difference in the interest= $9000- $6250

= $ 2750

5 0

2 years ago

CON PROCESOS POR FAVOR

labwork [276]

Answer:

$\dfrac{149}{40}$

$\dfrac{38}{15}$

Step-by-step explanation:

$(\dfrac{7}{8} + \dfrac{4}{5}) - (\dfrac{9}{20} + \dfrac{-5}{2}) =$

$= (\dfrac{7}{8} \times \dfrac{5}{5} + \dfrac{4}{5} \times \dfrac{8}{8}) - (\dfrac{9}{20} + \dfrac{-5}{2} \times \dfrac{10}{10})$

$= (\dfrac{35}{40} + \dfrac{32}{40}) - (\dfrac{9}{20} + \dfrac{-50}{20})$

$= \dfrac{67}{40} - (-\dfrac{41}{20})$

$= \dfrac{67}{40} + \dfrac{41}{20} \times \dfrac{2}{2}$

$= \dfrac{67}{40} + \dfrac{82}{40}$

$= \dfrac{149}{40}$

$(-\dfrac{6}{4} + \dfrac{3}{2}) + (\dfrac{6}{5} + \dfrac{4}{3}) =$

$= (-\dfrac{3}{2} + \dfrac{3}{2})+ (\dfrac{6}{5} \times \dfrac{3}{3} + \dfrac{4}{3} \times \dfrac{5}{5})$

$= 0 + \dfrac{18}{15} + \dfrac{20}{15}$

$= \dfrac{38}{15}$

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1 year ago

Prove that . 1+cot2 theta = cosec2theta​

Prove that . 1+cot2 theta = cosec2theta