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
All methods are supposed to be correct in most if not all situations and it should not matter if you use a different method given the options
Answer:
D.
Step-by-step explanation:
It is simply asking for the number that makes the equation untrue. So, all you need to do is plug in the various numbers below for w, and find out the incorrect number. Example with option D:
w-10≤16
27-10≤16
17≤16.
This makes the equation untrue, as 17 is not less than or equal to 16.
Hope this helps!
Answer:
y = - | (1/4)x - 1 | + 3
Step-by-step explanation:
if you are asking for the equation of the graph,
y = - | (1/4)x - 1 | + 3
Step-by-step explanation:
communitive property
