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
the value of the car will be 3250 after 5 years
Step-by-step explanation:
the value of the car = 13000
rate of interest = 15%
time = 5 years
in 5 years the car will depreciates = 13000 X 15% X 5
=
= 9750
after 5 years the value of the car is = 13000 - 9750 = 3250
Answer:
Step-by-step explanation:
We are given the two functions:
And we want to find:
This is equivalent to:
Substitute:
Distribute:
Rearrange:
Hence:
So what you do is theres 12 months so multiple that by 15 and get 180 then what you do is what time 80 equals 180 and thats your answer
Answer:
Step-by-step explanation:
C
