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Anestetic [448]
3 years ago
13

PageProve thatTan ( 2 Tan^-l x)=2 Tan ( Tan^-1 x + Tan^-1 x^3)​

Mathematics
1 answer:
Kay [80]3 years ago
5 0

Answer:

The answers are 0, 1 and −2.

Step-by-step explanation:

Let α=arctan(2tan2x) and β=arcsin(3sin2x5+4cos2x).

sinβ2tanβ21+tan2β2tanβ21+tan2β23tanxtan2β2−(9+tan2x)tanβ2+3tanx(3tanβ2−tanx)(tanβ2tanx−3)tanβ2=3sin2x5+4cos2x=3(2tanx1+tan2x)5+4(1−tan2x1+tan2x)=3tanx9+tan2x=0=0=13tanxor3tanx

Note that x=α−12β.

tanx=tan(α−12β)=tanα−tanβ21+tanαtanβ2=2tan2x−13tanx1+2tan2x(13tanx)or2tan2x−3tanx1+2tan2x(3tanx)=tanx(6tanx−1)3+2tan3xor2tan3x−3tanx(1+6tanx)

So we have tanx=0, tan3x−3tanx+2=0 or 4tan3x+tan2x+3=0.

Solving, we have tanx=0, 1, −1 or −2.

Note that −1 should be rejected.

tanx=−1 is corresponding to tanβ2=3tanx. So tanβ2=−3, which is impossible as β∈[−π2,π2].

The answers are 0, 1 and −2.

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The answer is <em><u>C,</u></em><em><u> </u></em><em><u>y=</u></em><em><u> </u></em><em><u>-</u></em><em><u>3</u></em><em><u>/</u></em><em><u>4</u></em><em><u> </u></em><em><u>+</u></em><em><u> </u></em><em><u>4</u></em>

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What is the proper seperation of factors for this equation ∛24n² × ∛36n²
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{ \tt{ \sqrt[3]{24 {n}^{2}  }  \times  \sqrt[3]{36 {n}^{2} } }} \\  = { \tt{(  {n}^{ \frac{2}{3} })( \sqrt[3]{864})  }}

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3 years ago
After a party, Brendan had left over pizza. Brendan had one half of a cheese pizza, 3/4 of a sausage pizza, and 2/6 of a peppero
muminat

3/4+2/6+1/2 = 9/12+4/12+6/12 = 19/12 Brendan has 1 7/12 leftover pizzas. THis is achieved by multiplying for a common denominator and adding

19/12-2/3 = 19/12-8/12 = 11/12 Brendan has 11/12 more pizzas than Steve.

8 0
3 years ago
A sports store sold a total of 59 footballs and soccer balls last weekend. Soccer balls cost $12 and footballs costs $18. If tot
lidiya [134]

Answer:ededikfgi34

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Someone pls help me I turn this in today the answer is there I just need to show work pls help me​
dolphi86 [110]

Hello and Good Morning/Afternoon

<u>Let's tale this problem step-by-step</u>:

<u>What does the problem want:</u>

 \hookrightarrow \text{the unemployment compensation}

<u>Employment compensation</u> =55% of the average of the last 26-week salary

  \hookrightarrow \text{Average of Natalia's salary} = (\text{all the salaries added up}) / (\text{number of weeks})\\\hookrightarrow \text{Average of Natalia's salary} = 18940 / 26 = 728.46 \text{ (Rounded down)}

         ⇒ 55% of that average

                \hookrightarrow \frac{55}{100} *728.46 = 400.65

<u>Answer: $400.65</u>

Hope that helps!

#LearnwithBrainly

5 0
1 year ago
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