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Nesterboy [21]
4 years ago
6

Prove the identity I NEED TO KNOW FAST AS POSSIBLE

Mathematics
1 answer:
antoniya [11.8K]4 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

sin²Θ = 1 - cos²Θ , cos²Θ = 1 - sin²Θ

Consider the left side

(sinΘ + cosΘ)(1 - sinΘcosΘ) ← distribute

= sinΘ(1 - sinΘcosΘ) + cosΘ(1 - sinΘcosΘ)

= sinΘ - sin²ΘcosΘ + cosΘ - sinΘcos²Θ

= sinΘ - (1 - cos²Θ)cosΘ + cosΘ - sinΘ(1 - sin²Θ)

= sinΘ - cosΘ + cos³Θ + cosΘ - sinΘ + sin³Θ ← collect like terms

= sin³Θ + cos³Θ

= right side ⇒ proven

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So,
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3 years ago
What is the measure of angle gxi?
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Answer:

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Step-by-step explanation:

4 0
3 years ago
4 consecutive numbers that add up to 8
Digiron [165]

Answer:

The answer top your question is: 1/2, 3/2, 5/2 and 7/2

Step-by-step explanation:

Data

4 consecutive numbers that add up to 8

First number = n

2nd number = n + 1

3rd number = n + 2

4th number = n + 3

Now, add them up           n + n + 1 + n + 2 + n + 3 = 8        

                                                                                          Simplify like terms

                                         4n + 6 = 8

                                         4n = 8 - 6

                                         4n = 2

                                         n = 2/4 = 1/2

First number = n         = 1/2

2nd number = n + 1    = 1/2 + 1 = 3/2

3rd number = n + 2    = 1/2 + 2 = 5/2

4th number = n + 3    = 1/2 + 3 = 7/2

8 0
3 years ago
Which way will the parabola open? Explain.
Marizza181 [45]
Our parabola open downward and therefore a is negative.

Explanation:
As value of a changes from positive to negative or from negative to positive, the direction of opening changes. For negative values of a we got negative parabolas that open downward. As the original formula y = x^2 we see that x^2 will always be positive because when you square a number it always gives positive value. Therefore the direction for which it will open, depends on value of a.
8 0
3 years ago
Read 2 more answers
Say you have $14,000 to invest into an investment account. You can either invest your money into an account with a 7% annual int
taurus [48]

Answer:

You should choose an account with a 7% annual interest rate which is compounded quarterly

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

part 1)

we have  

t=15\ years\\ P=\$14,000\\ r=0.07\\n=4  

substitute in the formula above  

A=14,000(1+\frac{0.07}{4})^{4*15}

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A=\$39,645.43  

part 2)

we have  

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substitute in the formula above  

A=14,000(1+\frac{0.068}{12})^{12*15}

A=14,000(1.0057)^{180}  

A=\$38,713.11  

7 0
3 years ago
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