sec(x)=1/cos(x), by definition of secant.
For any calculator Sec(Secant) = 1/Cos Csc (Cosecant) = 1/ Sin Cot (Cotangent) = 1/Tan
Sec(2x) = 1/Cos(2x)
sec x = 1/cos x → sec³ x = 1/cos³ x or sec³ x = (cos x)^-3 Therefore to enter sec³ x on a calculator: Newer, "natural" calculators: mathio: sec³ x → [x-power] [cos] [<angle>] [)] [navigate →] [(-)] [3] [=] lineio: sec³ x → [(] [cos] [)] [)] [x-power] [(-)] [3] [)] [=] Older, function acts on displayed number calculators: sec³ x → [angle] [cos] [x-power] [3] [±] [=]
zero
sec(x)=1/cos(x), by definition of secant.
Cos x = 1 / Sec x so 1 / Cos x = Sec x Then Tan x = Sin x / Cos x = Sin x * (1 / Cos x) = Sin x * Sec x
Yes, it is. the basic identity is for a double angle relation: cos 2x = 2 cosx cos x -1 since sec x =1/cos x if we multiply both sides by sec x we get cos2xsec x = 2cosxcos x/cos x -1/cos x = 2cos x - sec x
sec x = 1/cos x sec x cos x = [1/cos x] [cos x] = 1
Rewrite sec x as 1/cos x. Then, sec x sin x = (1/cos x)(sin x) = sin x/cos x. By definition, this is equal to tan x.
Prove that tan(x)sin(x) = sec(x)-cos(x) tan(x)sin(x) = [sin(x) / cos (x)] sin(x) = sin2(x) / cos(x) = [1-cos2(x)] / cos(x) = 1/cos(x) - cos2(x)/ cos(x) = sec(x)-cos(x) Q.E.D
sec x = 1/cos x so sec x * cos x = 1
Let 'theta' = A [as 'A' is easier to type] sec A - 1/(sec A) = 1/(cos A) - cos A = (1 - cos^2 A)/(cos A) = (sin^2 A)/(cos A) = (tan A)*(sin A) Then you can swap back the 'A' with theta
For any calculator Sec(Secant) = 1/Cos Csc (Cosecant) = 1/ Sin Cot (Cotangent) = 1/Tan
The answer is cos A . cos A = 1/ (sec A)
sec(x)=1/cos(x) - (hint: look at the third letter: sec->(1/)cos, cosec->(1/)sin, cot->(1/)tan)
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.