2h/3 -1/4 = 1/3 how do you do this problem

Prove that sinxtanx=1/cosx - cosx

maks197457 [2]

Answer:

See below

Step-by-step explanation:

We want to prove that

$\sin(x)\tan(x) = \dfrac{1}{\cos(x)} - \cos(x), \forall x \in\mathbb{R}$

Taking the RHS, note

$\dfrac{1}{\cos(x)} - \cos(x) = \dfrac{1}{\cos(x)} - \dfrac{\cos(x) \cos(x)}{\cos(x)} = \dfrac{1-\cos^2(x)}{\cos(x)}$

Remember that

$\sin^2(x) + \cos^2(x) =1 \implies 1- \cos^2(x) =\sin^2(x)$

Therefore,

$\dfrac{1-\cos^2(x)}{\cos(x)} = \dfrac{\sin^2(x)}{\cos(x)} = \dfrac{\sin(x)\sin(x)}{\cos(x)}$

Once

$\dfrac{\sin(x)}{\cos(x)} = \tan(x)$

Then,

$\dfrac{\sin(x)\sin(x)}{\cos(x)} = \sin(x)\tan(x)$

Hence, it is proved

5 0

3 years ago

Write a recursive rule for the sequence. 7, 6, 13, 19, 32, ...

Zinaida [17]

Answer:

Step-by-step explanation:

+7-1

4 0

3 years ago

A container is filled with water. This container has a small hole. After 20 minutes the amount of water in the container is 600

Grace [21]

Answer:

100 minutes and yes

Step-by-step explanation:

4 0

2 years ago

Robert went to the grocery store and purchased cans of soup and frozen dinners. each can of soup has 300 mg of sodium and each f

Paraphin [41]

There are 9 cans of soup and 5 cans of frozen dinner.

The variables used for soup and frozen dinner are x and y respectively.

Step-by-step explanation:

Let,

Soup = x

Frozen Dinner = y

According to given statement of sodium;

300x + 500y = 5200 eqn 1

And,

x + y = 14 eqn 2

$Multiplying\ equation\ 2\ with\ 300\\300(x+y=14)\\300x+300y=4200\ Eqn 3\\$

Subtracting Eqn 3 from Eqn 1;

$(300x+500y)-(300x+300y)=5200-4200\\300x+500y-300x-300y=1000\\200y=1000\\y=\frac{1000}{200} \\y=5$

Putting value of y in Eqn 1;

$300x+500(5)=5200\\300x+2500=5200\\\\Subtracting\ 2500\ from\ both\ sides\ \\300x+2500-2500=5200-2500\\300x=2700\\x=\frac{2700}{300} \\x=9$

There are 9 cans of soup and 5 cans of frozen dinner.

The variables used for soup and frozen dinner are x and y respectively.

Keywords: Variables, linear equations, subtraction.

Learn more about linear equations at;

#LearnwithBrainly

5 0

3 years ago

Phil can afford $200 a month for 5 years for a car loan. if the interest rate is 7.5 percent, how much can he afford to borrow t

madreJ [45]

200 per month for 5 years = 12,000
Phil can (at most) pay 12,000 for the car loan.
That would be the payment total.
So, how do we solve for the PRINCIPAL?
Looking at the attached formula, we see the
principal = Total - Total * ((1 +r)^-n) / r * n
where n = # of payments = 5 year * 12 months = 60 and
rate / 1.200 = 7.5/1,200 = .00625

principal = [12,000 - 12,000 * (1.00625)^-60] / .375
principal = [12,000 - 12,000 * 0.6880918239 ] / .375
principal = [12,000 - 8,257.1018863488] / .375
principal = 3,742.90 / .375
principal = 9,981.06

Source:
http://www.1728.org/loanfrm4.htm

6 0

3 years ago

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2h/3 -1/4 = 1/3how do you do this problem​

2h/3 -1/4 = 1/3how do you do this problem