Answer:
1/14
Step-by-step explanation:
There is only 1 common multiple of 4 and 6 between 1 and 14.
So the probability is:

Now, the cosecant of θ is -6, or namely -6/1.
however, the cosecant is really the hypotenuse/opposite, but the hypotenuse is never negative, since is just a distance unit from the center of the circle, so in the fraction -6/1, the negative must be the 1, or 6/-1 then.
we know the cosine is positive, and we know the opposite side is -1, or negative, the only happens in the IV quadrant, so θ is in the IV quadrant, now

recall that

therefore, let's just plug that on the remaining ones,

now, let's rationalize the denominator on tangent and secant,
Answer:
A, C
Step-by-step explanation:
Actually, those questions require us to develop those equations to derive into trigonometrical equations so that we can unveil them or not. Doing it only two alternatives, the other ones will not result in Trigonometrical Identities.
Examining
A) True

Double angle 
B) False,
No further development towards a Trig Identity
C) True
Double Angle Sine Formula 

D) False No further development towards a Trig Identity
![[sin(x)-cos(x)]^{2} =1+sin(2x)\\ sin^{2} (x)-2sin(x)cos(x)+cos^{2}x=1+2sinxcosx\\ \\sin^{2} (x)+cos^{2}x=1+4sin(x)cos(x)](https://tex.z-dn.net/?f=%5Bsin%28x%29-cos%28x%29%5D%5E%7B2%7D%20%3D1%2Bsin%282x%29%5C%5C%20sin%5E%7B2%7D%20%28x%29-2sin%28x%29cos%28x%29%2Bcos%5E%7B2%7Dx%3D1%2B2sinxcosx%5C%5C%20%5C%5Csin%5E%7B2%7D%20%28x%29%2Bcos%5E%7B2%7Dx%3D1%2B4sin%28x%29cos%28x%29)
The correct answer is option C.
The solution is shown below:
(8 - 3i)(6 + 5i)
= 8(6 +5i) - 3i(6 + 5i)
= 48 + 40i - 18i - 15i²
= 22i + 48 - 15(-1)
= 22i + 48 + 15
= 22i + 63
= 63 + 22i