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3 years ago

(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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Should be 6^3.

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3 years ago

Find the selling price of a $50 item after a 50 % markup

siniylev [52]

Answer:

75 dollars

Step-by-step explanation:

If an item is 50 and you want to markup 50%, you must find 50% of 50 to find how much the item will go up by from 50.

So 50% of 50 means 50% times 50.

50%=.5 or 1/2

So .5(50)=25.

The item is going up by 25 dollars.

So we started at 50 dollars.

So 50+25 is going to be the new amount.

50+25=75 is the new amount.

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3 years ago

Read 2 more answers

Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour

UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

$C(t) = C(0)e^{rt}$

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So $C(0) = 110$

Husband

Half life of 4 hours. So

$C(4) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{4r}$

$e^{4r} = 0.5$

Applying ln to both sides

$\ln{e^{4r}} = \ln{0.5}$

$4r = \ln{0.5}$

$r = \frac{\ln{0.5}}{4}$

$r = -0.1733$

So for the husband

$C(t) = 110e^{-0.1733t}$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.1733t}$

$C(11) = 110e^{-0.1733*11} = 16.35$

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

$C(10) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{10}$

$e^{10r} = 0.5$

Applying ln to both sides

$\ln{e^{10r}} = \ln{0.5}$

$10r = \ln{0.5}$

$r = \frac{\ln{0.5}}{10}$

$r = -0.0693$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.0693t}$

$C(11) = 110e^{-0.0693*11} = 51.33$

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

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4 years ago

How much is point (-24,-12) dilated by to get to (-18,-9)?

Anna [14]

Answer:

Dilation factor = 0.75.

Step-by-step explanation:

One point on the xy-plane is (-24,-12). The transformation is the dilation which is done on the point and the image is given by (-18,-9). Dilation changes the size of the shape according to the dilation factor. If the original x-coordinate is -24, then the image will be calculated by multiplying the original point with the dilation factor. Therefore, -18= -24 * k, where k is the unknown dilation factor. Simply solve the equation for k.

24k = 18.

k = 18/24 = 3/4 = 0.75.

Similarly, 12k = 9. k = 9/12 = 3/4 = 0.75.

So the point (-24,-12) dilated by k=0.75 to get to (-18,-9)!!!

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3 years ago

Frank started out in his car travelling 45 mph. When Frank was 1/3 miles away, Daniel started out from the same point at 50 mph

Anna007 [38]

Time taken by Daniel to catch up with Frank is 4 minutes.

Step-by-step explanation:

The question is on relative speed; speed of a moving object with respect to another.

The two cars are travelling in the same direction at different speeds thus;

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The time which the two meet = distance/ relative speed

Distance = 1/3 miles, which equals 0.33 miles

Time taken by Daniel to catch up with Frank is = 0.33/5 =0.066 hours = 4 minutes.

Learn More

Relative speed: brainly.com/question/10681729

Keywords: car, travelling, miles,started at the same point,catch up with

#LearnwithBrainly

6 0

4 years ago

Read 2 more answers

(1+tan^2 A)cot A/cosec^2 A= tanA​

(1+tan^2 A)cot A/cosec^2 A= tanA