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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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Sixty percent of the customers who go to Sears Auto Center for tires buy four tires and 22% buy two tires. Moreover, 12% buy few
kozerog [31]

Answer:

A Cumulative probability distribution for the number of tires bought is prepared below.

Step-by-step explanation:

We are given that Sixty percent of the customers who go to Sears Auto Center for tires buy four tires and 22% buy two tires. Moreover, 12% buy fewer than two tires, with 6% buying none.

The cumulative probability distribution for the number of tires bought is given by;

   <u>No. of tires</u>       <u>Probability Distribution</u>      <u>Cumulative Probability</u>

                                                                                    <u>Distribution</u>

           0                               6%                                             6%

           1                                6%                                             12%

           2                               22%                                           34%

           3                                6%                                             40%

           4                               60%                                           100%

Now, here we are given within the question about:

P(0 tires) = 6%

P(2 tires) = 22%

P(4 tires) = 60%  

Also, P(Fewer than 2 tires) = 12% which means P(0 tires) + P(1 tire) must be equal to 12%. So, P(1 tire) = 12% - 6% = 6%.

And, in the end P(3 tires) = 100% - 6% - 6% - 22% - 60% = 6%.

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