Answer:
The solutions of the equation are 0 , π
Step-by-step explanation:
* Lets revise some trigonometric identities
- sin² Ф + cos² Ф = 1
- tan² Ф + 1 = sec² Ф
* Lets solve the equation
∵ tan² x sec² x + 2 sec² x - tan² x = 2
- Replace sec² x by tan² x + 1 in the equation
∴ tan² x (tan² x + 1) + 2(tan² x + 1) - tan² x = 2
∴ tan^4 x + tan² x + 2 tan² x + 2 - tan² x = 2 ⇒ add the like terms
∴ tan^4 x + 2 tan² x + 2 = 2 ⇒ subtract 2 from both sides
∴ tan^4 x + 2 tan² x = 0
- Factorize the binomial by taking tan² x as a common factor
∴ tan² x (tan² x + 2) = 0
∴ tan² x = 0
<em>OR</em>
∴ tan² x + 2 = 0
∵ 0 ≤ x < 2π
∵ tan² x = 0 ⇒ take √ for both sides
∴ tan x = 0
∵ tan 0 = 0 , tan π = 0
∴ x = 0
∴ x = π
<em>OR</em>
∵ tan² x + 2 = 0 ⇒ subtract 2 from both sides
∴ tan² x = -2 ⇒ no square root for negative value
∴ tan² x = -2 is refused
∴ The solutions of the equation are 0 , π
I think you multiply them both from the area
Answer:
<em>P=0.0000037</em>
<em>P=0.00037%</em>
Step-by-step explanation:
<u>Probability</u>
A standard deck of 52 playing cards has 4 aces.
The probability of getting one of those aces is
Now we got an ace, there are 3 more aces out of 51 cards.
The probability of getting one of those aces is
Now we have 2 aces out of 50 cards.
The probability of getting one of those aces is
Finally, the probability of getting the remaining ace out of the 49 cards is:
The probability of getting the four consecutive aces is the product of the above-calculated probabilities:
P=0.0000037
P=0.00037%
4/9(2n)+4/9(-3)
(4x2/9)n+(4 x -3)/9
(8/9)n -12/9
8/9n-4/3
Answer:
Isosceles and scalene triangles can both be obtuse.
