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swat32
3 years ago
7

(1+tan^2 A)cot A/cosec^2 A= tanA​

Mathematics
1 answer:
Rufina [12.5K]3 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

1 + tan²A = sec²A , secA = \frac{1}{cosA}, cosecA = \frac{1}{sinA} , cotA = \frac{cosA}{sinA} , tanA = \frac{sinA}{cosA}

Consider the left side

\frac{(1+tan^2A)cotA}{cosec^2A}

= \frac{sec^2AcotA}{cosec^2A}

= \frac{\frac{1}{cos^2A}(\frac{cosA}{sinA})  }{cosec^2A}

= \frac{\frac{1}{cosAsinA} }{\frac{1}{sin^2A} }

= \frac{1}{cosAsinA} × sin²A

= \frac{sinA}{cosA}

= tanA = right side , thus proven

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3 years ago
An ellipse is centered at the origin. Find it’s equation.
MA_775_DIABLO [31]

Answer:

(x)^2        (y)^2

---------- + --------- = 1

 4              3

Step-by-step explanation:

The standard equation for an ellipse is

(x-h)^2     (y-k)^2

---------- + --------- = 1

a^2            b^2

The center is at (h,k)

The vertices are at (h±a, k)

The foci are at (h±c,k )

Where c is sqrt(a^2 - b^2)

It is centered at the origin so h,k are zero

(x)^2        (y)^2

---------- + --------- = 1

a^2            b^2

The center is at (0,0)

The vertices are at (0±a, 0)

The foci are at (0±c,0 )

The vertices are (±2,0)  so a =2

The foci is 1

c = sqrt(a^2 - b^2)

1 = sqrt(2^2 - b^2)

Square each side

1 = 4-b^2

Subtract 4 from each side

1-4 = -b^2

-3 = -b^2

3= b^2

Take the square root

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---------- + --------- = 1

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3 years ago
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I’m pretty sure the answer is C
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Read 2 more answers
Teagan is dividing 6 by 11. If she continues the process, what will keep repeating in the quotient? The sequence 05 Only the dig
Oksi-84 [34.3K]

Answer:

Teagan is dividing 6 by 11. If she continues the process, what will keep repeating in the quotient?

The sequence 05

Only the digit 5

The sequence 54

Only the digit 4

The sequence 54  is the final answer.

Step-by-step explanation:

Given:

A a fraction 6/11 which Teagan is dividing we have to find the repeating quotient.

Here the divisor is 11 and the dividend is 6.

Lets say that the quotient is "q" .

And we know that:

⇒ Dividend / divisor = quotient

Or

In mixed fraction.

⇒ Dividend / divisor = quotient + (remainder/ divisor)

Finding the values of "q".

⇒ \frac{Dividend}{divisor} = quotient

⇒ \frac{6}{11} = 0.5454....

Explanation:

  • To divide 6 with 11 we have to take a decimal in quotient which allows us to have a zero in each step in the quotient.
  • After putting zero the dividend will become 60 and then we can apply 11\times 5 = 55 ...5 in the quotient and 55 in the numerator.
  • In third step we will subtract 55 with 60 that will give us 5 putting a zero with it it will be now 50 ,and the closet multiple of 11 is 11\times 4=44, 4 with the quotient and and 50-44=06 will continue to be divided.
  • The fraction is a rational numbers as the decimals occurring are repeating decimals in the quotient.

Our final answer from the option is : C

The sequence 54 will be repeating.

4 0
4 years ago
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