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vovikov84 [41]
4 years ago
12

Prove identity: Sec^6x-tan^6x= 1+3tan^2xsec^2x

Mathematics
1 answer:
Kisachek [45]4 years ago
7 0
<span>This time, we start from the left side.
sec^6x-tan^6x =(sec^2x)^3-(tan^2x)^3

Then, use the identity:

a^3-b^3 = (a-b)(a^2+ab+b^2)

we get (sec^2x-tan^2x)(sec^4x+sec^2x tan^2x+ tan^4x)
Since (tan^2x+1=sec^2x)
We have \((\sec^2x-\tan^2x) = 1\).

So, (sec^2x-tan^2x)(sec^4x+sec^2x tan^2x+tan^4x)
(=sec^4x+sec^2xtan^2x+tan^4x)

Then consider (sec^4x), (sec^4x = sec^2x (sec^2x) = sec^2x(tan^2x+1) = sec^2x tan^2x+ sec^2x)

Consider (tan^4x), (tan^4x = tan^2x (tan^2x) = tan^2x(sec^2x+1) = sec^2x tan^2x- tan^2x)

Substitute the two back to (sec^4x+sec^2x tan^2x+tan^4x, and simplify it.

With the help of the identity sec^2x-tan^2x = 1, you should be able to get the right side.</span>
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You want to join the tennis team. You go to the sporting goods store with $100. If the tennis racket you want costs $80 and the
Juli2301 [7.4K]

Answer: You can buy 5 cans of tennis balls.

Step-by-step explanation: 100 minus 80 is 20 and that leaves $20 for tennis balls, so 20 divided by 4 is 5 and that's how many cans you can buy.

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3 years ago
Find the slope for -8y=2x+5
Anastasy [175]

Answer:

-1/4

Step-by-step explanation:

in y=mx+b, m represents the slope. Let's try to get your equation to look like that. We can see that on the left side, the y is not yet alone so we must try to accomplish that. to do that we divide by -8 from the -8y, but we must also do that to the other side. you would get y=-2/8x-5/8. then we would simplify the -2/8x into -1/4x. Now it is y=-1/4x-5/8 and that resembles y=mx+b. m is slope and -1/4 is m.

4 0
3 years ago
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Multiply the fractions:<br> 2 / 5 ∙ 3 / 4.
Bingel [31]

Answer:

\frac{3}{10}

Step-by-step explanation:

\frac{2}{5} * \frac{3}{4} can be solved by just multiplying the numerators together and the denominators together

2 * 3 = 6 and 5 * 4 = 20 so the answer would be \frac{6}{20}

This simplifies to \frac{3}{10}

4 0
4 years ago
Tiana deposited $500 into an account that earns 6% simple interest. How many years will it take for the value of the account to
Mkey [24]

Answer:

In 50 years the amount will be $ 2000.

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Tiana deposited $500 into a account at 6 % simple interest per Year .

3 0
3 years ago
There are 6 white and 3 orange ping-pong balls in a brown paper bag. Two balls are randomly chosen. Enter your answers as fracti
Masteriza [31]

Answer:

a. 9

b. \mathbf{\frac{1}{3}}

c. \mathbf{\frac{1}{4}}

d. \mathbf{\frac{1}{12}}

Step-by-step explanation:

a. The total number of balls in the bag is

6 + 3 = 9

b. Let A denote the event that the 1st chosen ball is orange. Let B denote the event that the 2nd chosen ball is orange.

P(A) = \frac{\text{no. of orange balls in the bag}}{\text{Total no. of balls}} = \frac{3}{9} = \mathbf{\frac{1}{3}}

c. If the first choice is orange, (i.e A occurs) then there are 9 - 1 = 8 balls left in the bag with 3 - 1 = 2 orange balls.

P(B|A) = \frac{2}{8} = \mathbf{\frac{1}{4}}

d. Here we are required to compute P(B \cap A). We use the fact that

P(B|A) = \frac{P(B \cap A)}{P(A)} \implies P(B \cap A) = P(B | A) \times P(A) = \frac{1}{4} \times \frac{1}{3} = \mathbf{\frac{1}{12}}

4 0
4 years ago
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