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3 years ago

Sin^4a+cos^4a -sin^6a+cos^6a= sin^2a cos^2a

Mathematics

1 answer:

dsp733 years ago

7 0

Answer:

steps below

Step-by-step explanation:

sin⁴a+cos⁴a = (sin²a+cos²a)² - 2 sin²a cos²a

= 1 - 2 sin²a cos²a

sin⁶a-cos⁶a = (sin²a+cos²a)³ - 3 sin²a cos²a (sin²a + cos²a)

= 1³ - 3 sin²a cos²a * 1

= 1 - 3 sin²a cos²a

sin⁴a+cos⁴a-sin⁶a+cos⁶a = (1 - 2 sin²a cos²a) -(1 - 3 sin²a cos²a)

= sin²a cos²a

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Julie had 2730 cards and Kim had 3570 cards at first.

Anna71 [15]

Answer:

1155

Step-by-step explanation:

Total number of cards is 2730+3570=6300

Since Kim now has 3 times the card of Julie so Julie must have 6300/4=1575.

So, Julie gave 2730-1575=1155

4 0

3 years ago

Read 2 more answers

6<br><br><br> math geniuses help please!!<br><br><br> math

damaskus [11]

Answer:

Step-by-step explanation:

Begin with Euler's formula. I am assuming youre aware of this if youre taking complex algebra? You can prove Euler's formula by doing a Maclaurin expansion of cosine, sine, and e^x. Euler's formula states that:

$e^{ix}=cos(x)+isin(x)$

We can put the first complex number in exponetial form by noticing the input is 2pi/3. The second complex number has an input of pi/3. Therefore:

$z_1=8e^{i(2\pi /3)}$

$z_2=0.5e^{i(\pi /3)}$

Then:

$\frac{z_1}{z_2} =\frac{8e^{i(2\pi /3)}}{0.5e^{i(\pi /3)}}$

Simplify the coefficients to get:

$\frac{z_1}{z_2} =\frac{16e^{i(2\pi /3)}}{e^{i(\pi /3)}}$

When you divide exponentials, you subtract the exponents. Therefore:

$\frac{z_1}{z_2} =16e^{i(2\pi /3)-i(\pi /3)}=16e^{i(\pi /3)$

Put it back into trigonemtric form using Euler's formula:

$16e^{i(\pi /3)}=16cos(\pi /3)+i16sin(\pi /3)$

Cosine of pi/3 is 0.5, and sine of pi/3 is square root of 3 over 2. We have:

$16e^{i(\pi /3)}=16cos(\pi /3)+i16sin(\pi /3)=16*0.5+16*\frac{\sqrt{3} }{2} *i=8+8\sqrt{3} i$

5 0

2 years ago

Converges or Diverges: Please help me

bagirrra123 [75]

Use a/ 1-r

Where a = 18 and r = 1.2

18/ 1 - 1.2 = 18/-.2 = -90

Because the answer is below 1. The sum does not exist therefore it diverges.

8 0

4 years ago

Brandy solved 1/6/ 5 using a related multiplication expression. What multiplication expression did she use?

Advocard [28]

<h3><u>Question:</u></h3>

Brandy solved 1/6÷ 5 by using a related multiplication expression. which multiplication expression did she use

<h3><u>Answer:</u></h3>

The expression that she can use is $\frac{1}{6} \times \frac{1}{5}$

<h3><u>Solution:</u></h3>

<em><u>Given that Brandy solved the following expression</u></em>

$\frac{1}{6} \div 5$

We have to find the multiplication expression she used

From given expression,

$\frac{1}{6} \div 5$

We can convert the division symbol to multiplication

Convert the fraction division process to a multiplication process by using the following steps:

Change the “÷” (division sign) to “x” (multiplication sign) and invert the number to the right of the sign.

Multiply the numerators. Multiply the denominators

Therefore,

$\frac{1}{6} \div 5 = \frac{1}{6} \times \frac{1}{5}$

$\frac{1}{6} \div 5 = \frac{1}{6} \times \frac{1}{5} = \frac{1}{30}$

Thus, the expression that she can use is $\frac{1}{6} \times \frac{1}{5}$

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3 years ago

A country's population in 1995 was 56 million in 2002 it was 59 million estimate the population in 2016

storchak [24]

65 million would be the population in 2016

7 0

3 years ago