Lucifer the angel became God's "adversary" [Satan] when he sinned [transgressed God's Commandments; His laws- I John 3:4] in the beginning... before man was created.
"I ordained and anointed you as the Mighty Angelic Guardian. You had access to the Holy Mountain of God... You were blameless in all you did from the day you were created UNTIL THE DAY EVIL WAS FOUND IN YOU... So I banished you from the Mountain of God. I expelled you, O Mighty Guardian... I threw you to the earth ..." (Ezek.28:14-17 NLT New Living Translation)
"...I saw Satan falling from heaven as a flash of lightning!" (Luke 10:18 NLT)
"For you said to yourself, 'I will ascend to heaven and rule the angels. I will take the Highest Throne... I will climb to the highest heavens and be like the Most High..." (Isa.14:13-14 LVB Living Bible).
"Then there was war in heaven... And the Dragon lost the battle and was forced from heaven." (Rev.12:7-8 LVB)
Satan sinned FIRST!
"...HE WAS A MURDERER FROM THE BEGINNING and a hater of the Truth [God's Word - John 17:17] -- there is not one iota of Truth in him. When he lies, it is perfectly normal, forhe is theFATHER [the ORIGINATOR; the progenitor] of liars." (John 8:44 LVB Living Bible)
People tend to think that "man" [rather, Eve] sinned first.And she was the first of "mankind" to be deceived by Satan.In the Genesis chapter 3 account... it wasn't the untainted and perfect "Lucifer" who confronted Eve, but: "...the ancient Serpent called the Devil, or Satan, the one deceiving the whole world..." (Rev.12:9 LVB) -- previously "fallen from heaven" and ready to temp and open the minds and hearts of the first two people created in God's image to rebellion and disobedience. Ready and waiting to lead them astray.
"...for your eyes will be opened -- you will be able to distinguish good from evil!" (Gen.3:5 LVB)
"You... were just like all the others, full of sin, OBEYING SATAN, the mighty prince of the power of the air, who is at work right now in the hearts of those who are against the Lord." (Eph.2:2 LVB)
Cotangent = 1/Tangent : Cosecant = 1/Sine Then, cot + 1 = (1/tan) + 1 = (cos/sin) + (sin/sin) = (cos + sin)/ sin. Now, cos² + sin² = 1 so for the statement to be valid the final expression would have to be : (cos² + sin² ) / sin = 1/sin. As this is not the case then, cot + 1 ≠ cosec. In fact, the relationship link is cot² + 1 = cosec²
Well I don't exactly get "the solution", but simplifying the equation is quite simple. Maybe that's what you're looking for. Here are the steps for simplifying it. costancsc = 1 1. Change tan to sin/cos 2. Change csc to 1/sin cos(sin/cos)(1/sin) = 1 And as you can now see, the first cos cancels with the second one under the sin/cos fraction, and the first sin cancels with the second one under the 1/sin fraction consequentially leaving you with 1 = 1. For a better look, notice this fraction when all three parts are combined cos * sin * 1 ---------------- cos * sin See how the cos and sin cancel each other leaving you with 1 * 1 * 1 which is just 1. Therefore the final simplification is just 1 = 1. I hope this helps!
2 sin^2 theta = 1/4 sin^2 theta = 1/8 sin theta = sqrt(1/8) theta = arcsin(sqrt(1/8))
[sin - cos + 1]/[sin + cos - 1] = [sin + 1]/cosiff [sin - cos + 1]*cos = [sin + 1]*[sin + cos - 1]iff sin*cos - cos^2 + cos = sin^2 + sin*cos - sin + sin + cos - 1iff -cos^2 = sin^2 - 11 = sin^2 + cos^2, which is true,
It's pronounced Sin-Wall or Sin-Wool.
cos2 x /(1 - sin x)= (1 - sin2 x )/(1 - sin x)= (1 + sin x)(1 - sin x)/(1 - sin x)= 1 + sin x
cos x / (1-sin x) = cos x (1 + sin x) / (1 - sin x) (1 + sin x) = cos x (1 + sin x) / (1 - sin2x) = cos x (1 + sin x) / cos2 x = (1 + sin x) / cos x = sec x + tan xcos x / (1-sin x) = cos x (1 + sin x) / (1 - sin x) (1 + sin x) = cos x (1 + sin x) / (1 - sin2x) = cos x (1 + sin x) / cos2 x = (1 + sin x) / cos x = sec x + tan xcos x / (1-sin x) = cos x (1 + sin x) / (1 - sin x) (1 + sin x) = cos x (1 + sin x) / (1 - sin2x) = cos x (1 + sin x) / cos2 x = (1 + sin x) / cos x = sec x + tan xcos x / (1-sin x) = cos x (1 + sin x) / (1 - sin x) (1 + sin x) = cos x (1 + sin x) / (1 - sin2x) = cos x (1 + sin x) / cos2 x = (1 + sin x) / cos x = sec x + tan x
sin x times sin x. or 1/cosec2(x) or 1 - cos2(x) or tan2(x)*cos2(x) etc, etc.
sec + tan = cos /(1 + sin) sec and tan are defined so cos is non-zero. 1/cos + sin/cos = cos/(1 + sin) (1 + sin)/cos = cos/(1 + sin) cross-multiplying, (1 + sin)2 = cos2 (1 + sin)2 = 1 - sin2 1 + 2sin + sin2 = 1 - sin2 2sin2 + 2sin = 0 sin2 + sin = 0 sin(sin + 1) = 0 so sin = 0 or sin = -1 But sin = -1 implies that cos = 0 and cos is non-zero. Therefore sin = 0 or the solutions are k*pi radians where k is an integer.
Roman Catholic AnswerNo, "He who knows his brother is committing a sin that is not until death, shall ask, and shall give life to him who does not commit a sin unto death. There is a sin unto death; I do not mean that anyone should ask as to that." 1 St. John 5:16 (Douay-Rheims) The sin unto death is mortal, the sin not unto death is venial. Venial is the Church's word for it, but the construct is Biblical, read St. John's first letter.
sin theta = opp/hyp sin 45 = opp/1 opp = sin 45 = sqrt(2)/2 ~= 0.7071
(tan x - sin x)/(tan x sin x) = (tan x sin x)/(tan x + sin x)[sin x/cos x) - sin x]/[(sin x/cos x)sin x] =? [(sin x/cos x)sin x]/[sin x/cos x) + sin x][(sin x - sin x cos x)/cos x]/(sin2 x/cos x) =? (sin2 x/cos x)/[(sin x + sin x cos x)/cos x)(sin x - sin x cos x)/sin2 x =? sin2 x/(sin x + sin x cos x)[sin x(1 - cos x)]/sin2 x =? sin2 x/[sin x(1 + cos x)(1 - cos x)/sin x =? sin x/(1 + cos x)(1 - cos x)/sin x =? [(sin x)(1 - cos x)]/[(1 + cos x)(1 - cos x)](1 - cos x)/sin x =? [(sin x)(1 - cos x)]/[1 - cos2 x)(1 - cos x)/sin x =? [(sin x)(1 - cos x)]/[1 - (1 - sin2 x)](1 - cos x)/sin x =? [(sin x)(1 - cos x)]/sin2 x(1 - cos x)/sin x = (1 - cos x)/sin x True