Answer: 0, π, 2π
Nevertheless, that is not an option. I see two possibilities: 1) the options are misswirtten, 2) the domain is not well defined.
If the domain were 0 ≤ θ < 2π, then 2π were excluded of the domain ant the answer would be 0, π.
Explanation:
1) The first solution, θ = 0 is trivial:
sin (0) - tan (0) = 0
0 - 0 = 0
2) For other solutions, work the expression:
sin(θ) + tan (-θ) = 0 ← given
sin (θ) - tan(θ) = 0 ← tan (-θ) = tan(θ)
sin(θ) - sin (θ) / cos(θ) = 0 ← tan(θ) = sin(θ) / cos(θ)
sin (θ) [1 - 1/cos(θ)] = 0 ← common factor sin(θ)
⇒ Any of the two factors can be 0
⇒ sin (θ) = 0 or (1 - 1 / cos(θ) = 0,
sin(θ) = 0 ⇒ θ = 0, π, 2π
1 - 1/cos(θ) = 0 ⇒ 1/cos(θ) = 1 ⇒ cos(θ) = 1 ⇒ θ = 0, 2π
⇒ Solutions are 0, π, and 2π
In fact if you test with any of those values the equation is checked. The only way to exclude one of those solutions is changing the domain.
1/4 (a) = (2/3)
a = (2/3) * (4)
a=8/3
a= 2 2/3
Answer: one third. one half and 1 whole
Step-by-step explanation:
Answer:
I think B.
Step-by-step explanation:
Answer:
Explanation:
All the other expressions can be factorized. Let's see why:
1) 
This is the sum of the cubes, and this can be factorized as follows:
In this case, a=m and b=1, so we can factorize as
2) 
This is the difference between two cubes, and this can be factorized as follows:
In this case, a=m and b=1, so we can factorize as
3) 
This is the difference between two square numbers, and it can be factorized as follows
In this case, a=m and b=1, so we can factorize as
