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sukhopar [10]
3 years ago
10

Prove tan(θ / 2) = sin θ / (1 + cos θ) for θ in quadrant 1 .

Mathematics
2 answers:
Leona [35]3 years ago
3 0
We are asked to prove tan(θ / 2) = sin θ / (1 + cos θ). In this case, tan θ is equal to sin θ / cos θ. we can apply this to the equality. sin θ is equal to square root of (1-cos θ)/2 while cos θ is equal to <span>square root of (1 + cos θ)/2.
Hence, when we replace cos </span><span>θ with </span>square root of (1-cos θ)/2, we can prove already.
Novay_Z [31]3 years ago
3 0

Answer:

Step-by-step explanation:

We have to prove the identitytan(\frac{\Theta }{2})=\frac{sin\Theta}{1+cos\Theta }

We will take right hand side of the identity

\frac{sin\Theta}{1+cos\Theta}=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{1+[2cos^{2}(\frac{\Theta }{2})-1]}

=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{2cos^{2}(\frac{\Theta }{2})}=\frac{sin(\frac{\Theta }{2})}{cos(\frac{\Theta }{2})}

=tan(\frac{\Theta }{2}) [ Tan θ will be positive since θ lies in 1st quadrant ]

= L. H. S.

Hence proved.

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How are the volume formulas of prisms and cylinders similar? How are they<br> different?
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Answer:

They are both similar in the way that the formula is base multiplied by height. They are different because of the type of shape on the base.

Step-by-step explanation:

hope this helps

7 0
3 years ago
Solve and graph each of the following. Show your work to receive full credit.5x – 6 – 8x ≤ 9
alexandr402 [8]

Answer: x> or equal to -5

Step-by-step explanation:

5x – 6 – 8x ≤ 9

Combine the lioe numbers

-3x-6≤ 9

+6 to both sides

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Divide by a -3 to both sides

X>or equal to -5

Hope that helps

4 0
3 years ago
You are drawing two cards, without replacement, from a standard deck of 52 cards. What is the
Serga [27]

Answer:

Dear student,

Answer to your query is provided below

Probability of drawing a 2 at first is (4/52) = (1/13)

Probability of drawing a face card in second try without replacement = 12/51

Step-by-step explanation:

Total no. Of cards = 52

Total no. Of cards of 2 = 4

Prob. Of drawing 2 = 4/52

Total no. Of face card = 12

Total no.of cards left in deck = 51

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5 0
3 years ago
DeSean is sorting his toy car collection. ⅔ of the cars are sports cars. ¼ of the remaining toys are pick up trucks. All of the
user100 [1]

Answer:

Fraction of fire trucks = \frac{1}{4}

Total number of toy cars = 16

Step-by-step explanation:

Fraction of sports car = \frac{2}{3}

Fraction of remaining cars =1-\frac{2}{3}=\frac{3-2}{3} =\frac{1}{3}

So,

Fraction of pick up cars = \frac{1}{4}(\frac{1}{3})=\frac{1}{12}

Therefore,

Fraction of fire trucks = \frac{1}{3}-\frac{1}{12}=\frac{4-1}{12}=\frac{3}{12}=\frac{1}{4}

That is Number of fire trucks = \frac{1}{4} ( Total number of toy cars )

Number of fire trucks = 4

Total number of toy cars = 4(4)=16

3 0
3 years ago
would you prefer to purchase a cheap car which cost more to operate or to purchase a expensive car which cost less to operate? w
alexandr402 [8]

Answer: Expensive car which cost less to operate.


Step-by-step explanation: When purchasing a new expensive car it is much more reliable, the risk you run with buying a used car is it breaking down on you while you are driving. Much less likely to happen with a new car.


5 0
4 years ago
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