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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)

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โˆ™ 2012-01-05 14:07:12
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Q: Sec - cos equals tansin
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Cos plus tansin equals sec?

Start on the left-hand side. cos(x) + tan(x)sin(x) Put tan(x) in terms of sin(x) and cos(x). cos(x) + [sin(x)/cos(x)]sin(x) Multiply. cos(x) + sin2(x)/cos(x) Make the denominators equal. cos2(x)/cos(x) + sin2(x)/cos(x) Add. [cos2(x) + sin2(x)]/cos(x) Use the Pythagorean Theorem to simplify. 1/cos(x) Since 1/cos(x) is the same as sec(x)- the right-hand side- the proof is complete.


Should we find cos theta if sec theta equals -10?

No.


1 over cos x equals what?

sec(x)=1/cos(x), by definition of secant.


How do you solve Sin x sec x equals tan x?

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


Is cos 2 x sec x equals 2 cos x - sec x an identity?

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


What is the reciprocal function of sec A?

The answer is cos A . cos A = 1/ (sec A)


What is sec x cos x?

sec x = 1/cos x sec x cos x = [1/cos x] [cos x] = 1


What is the population of Tansin?

The population of Tansin is 646.


How do you put sec in a TI 84 calculator?

sec = 1 / cos sec = 1 / cos


How do you find sec x cos x?

sec x = 1/cos x so sec x * cos x = 1


How do you identify sec x sin x equals tan x?

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.


What is sec theta - 1 over sec theta?

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


What is 2 by cos a?

2/cos(a) = 2 sec(a)


How do you put sec cubed in a calculator?

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] [±] [=]


Find the principal solution of sec x equals 2?

sec(x) = 2 so cos(x) = 1/2 and so x = pi/3


What is sec2x in relationship to cos?

Sec(2x) = 1/Cos(2x)


How do you prove that the derivative of sec x is equal to sec x tan x?

Show that sec'x = d/dx (sec x) = sec x tan x. First, take note that sec x = 1/cos x; d sin x = cos x dx; d cos x = -sin x dx; and d log u = du/u. From the last, we have du = u d log u. Then, letting u = sec x, we have, d sec x = sec x d log sec x; and d log sec x = d log ( 1 / cos x ) = -d log cos x = d ( -cos x ) / cos x = sin x dx / cos x = tan x dx. Thence, d sec x = sec x tan x dx, and sec' x = sec x tan x, which is what we set out to show.


How do you calculate sec in trigonometry?

sec(x)=1/cos(x) - (hint: look at the third letter: sec->(1/)cos, cosec->(1/)sin, cot->(1/)tan)


How do you solve the following identity sec x - cos x equals sin x tan x?

sec x - cos x = (sin x)(tan x) 1/cos x - cos x = Cofunction Identity, sec x = 1/cos x. (1-cos^2 x)/cos x = Subtract the fractions. (sin^2 x)/cos x = Pythagorean Identity, 1-cos^2 x = sin^2 x. sin x (sin x)/(cos x) = Factor out sin x. (sin x)(tan x) = (sin x)(tan x) Cofunction Identity, (sin x)/(cos x) = tan x.


1 over cos y is equal to?

1/cos y = sec y


How do you prove tan x plus tan x sec 2x equals tan 2x?

tan x + (tan x)(sec 2x) = tan 2x work dependently on the left sidetan x + (tan x)(sec 2x); factor out tan x= tan x(1 + sec 2x); sec 2x = 1/cos 2x= tan x(1 + 1/cos 2x); LCD = cos 2x= tan x[cos 2x + 1)/cos 2x]; tan x = sin x/cos x and cos 2x = 1 - 2 sin2 x= (sin x/cos x)[(1 - 2sin2 x + 1)/cos 2x]= (sin x/cos x)[2(1 - sin2 x)/cos 2x]; 1 - sin2 x = cos2 x= (sin x/cos x)[2cos2 x)/cos 2x]; simplify cos x= (2sin x cos x)/cos 2x; 2 sinx cos x = sin 2x= sin 2x/cos 2x= tan 2x


What is the reciprocal of a cosine?

1/cos(x)=sec(x). sec is short for secant.


What is the solution to cos equals sec-sintan?

I'm not really sure what you mean by "the solution", but that equation cos = sec - sintan does simplify down to sin^2 + cos^2 = 1 which so happens to be an identity. I'm not sure if that's what you're looking for, but if it is, here are the steps in simplifying it. 1. Convert sec to 1/cos 2. Convert tan into sin/cos and multiply it by sin sintan = sin(sin/cos) = (sin^2)/cos You then have cos = 1/cos - (sin^2/cos) 3. Multiply everything by cos cos^2 = 1 - sin^2 4. And finally, send the sin^2 over to the left side by adding it (since it is being subracted on the right) You should see this sin^2 + cos^2 = 1 which is an identity.


If cos x equals 1 what is the value of sec x?

Secant x= 1/cosx So if cos x=1 ,we know that x=0 degrees ( or radians), so secant x is 1/cos (0)=1/1=1


What is the solution to sec plus tan equals cos over 1 plus sin?

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.