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I'm not sure what u mean by solving an identity. An identity is an equation that is always true, i.e., true for all values of the variable(s), in this case x. The only thing u can do with an identity is to prove that it is an identity. The problem here is that it is not an identity. Since sec x = 1 / cos x, the left side of the equation, when defined, is always = 1 (it is not defined when cos x = 0, because u cannot divide by 0). The right side, since tan x = sin x / cos x, is = sin2 x / cos x. When x = 0, the right side = 0 / 1 = 0. So it is not an identity.
Perhaps u meant how do u solve the equation. That is a completely different question, which means find what values of x makes the equation true. In this case, we need to find when the right side is = 1, so sin2 x = cos x (but not 0). Since sin2 x = 1 - cos2 x, this amounts to 1 - cos2 x = cos x, or 1 - cos2 x - cos x = 0. This is a quadratic equation in cos x, whose solutions are cos x = 0.61803398874989484820458683436564 and cos x = -1.6180339887498948482045868343656. The latter never happens (for real x), because cos x is always between -1 and 1. The other happens when x = 51.82729237298775250653169866715 degrees. This turns out to be, I believe, the arc cosine of the golden ratio.
Correction: 0.61803398874989484820458683436564 is actually the reciprocal of the golden ratio, so the answer I gave above is the arc sine of the golden ratio. Also, it is not the only solution. Subtracting it from 360 degrees gives 308.17270762701224749346830133285 degrees, which is another solution. Adding or subtracting any multiple of 360 degrees to or from either of those solutions will also work, since all trig functions are periodic with period 2 pi radians, or 360 degrees.
"Dingbot suspects that this answer contains gibberish". Dingbot is wrong - it looks fine to me.
My only reservation is the excess of precision. Surely four to six significant figures are enough (!). It's probably time to stop slavishly copying answers from Windows Calculator.
You're right. That's where I got the numbers from. I just thought that since this is not a physical measurement but a number that is the solution to a pure math equation, all the digits it gives me (except maybe the last one) are correct, so I might as well use what I have, rather than try to decide how many digits of precision to round to. I'll keep that in mind for future reference.
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How do you verify the identity of cos θ tan θ equals sin θ?
To show that (cos tan = sin) ??? Remember that tan = (sin/cos) When you substitute it for tan, cos tan = cos (sin/cos) = sin QED
Is 1- cos 2 x 1 plus cos 2 x equals sin squared x cos squared x an identity?
No, (sinx)^2 + (cosx)^2=1 is though
How do you solve trignometric identities?
tan(x) = sin(x)/cos(x) Therefore, all trigonometric ratios can be expressed in terms of sin and cos. So the identity can be rewritten in terms of sin and cos. Then there are only two "tools": sin^2(x) + cos^2(x) = 1 and sin(x) = cos(pi/2 - x) Suitable use of these will enable you to prove the identity.
How do you solve secant-tangent and tangent-tangent angles?
you solve secant angles when you have the hypotenuse and adjacent sides. sec=1/cos or, cos^-1 (reciprocal identity property) Tangent is solved when you have adjacent and opposite sides, or you can look at it as its what you use when you dont have the hypotenuse. tan=sin/cos or tan=opp/adj or tan=y/x
Prove that secB - cosB equals tanBsinB?
Try to write everything in terms of sines and cosines:1 / cos B - cos B = (sin B / cos B) sin B1 / cos B - cos B = sin2B / cos BMultiply by the common denominator, cos B:1 - cos2B = sin2BUse the pithagorean identity on the left side:sin2B + cos2B - cos2B = sin2Bsin2B = sin2B
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.
How do you verify the identity of cos θ tan θ equals sin θ?
To show that (cos tan = sin) ??? Remember that tan = (sin/cos) When you substitute it for tan, cos tan = cos (sin/cos) = sin QED
If cos and theta 0.65 what is the value of sin and theta?
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
Solve Cos x - 1 equals 0?
cos x - 1 = 0 cos(x) = 1 x = 0 +/- k*pi radians where k = 1,2,3,...
Is 1- cos 2 x 1 plus cos 2 x equals sin squared x cos squared x an identity?
No, (sinx)^2 + (cosx)^2=1 is though
How do you solve trignometric identities?
tan(x) = sin(x)/cos(x) Therefore, all trigonometric ratios can be expressed in terms of sin and cos. So the identity can be rewritten in terms of sin and cos. Then there are only two "tools": sin^2(x) + cos^2(x) = 1 and sin(x) = cos(pi/2 - x) Suitable use of these will enable you to prove the identity.
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
How do you solve the equation cos2x plus 20 equals negative half?
Better formatting is cos(2x+20)=-0.5
How do you solve secant-tangent and tangent-tangent angles?
you solve secant angles when you have the hypotenuse and adjacent sides. sec=1/cos or, cos^-1 (reciprocal identity property) Tangent is solved when you have adjacent and opposite sides, or you can look at it as its what you use when you dont have the hypotenuse. tan=sin/cos or tan=opp/adj or tan=y/x
Sin Squared x plus cos x equals 0 for x is a part of 1 to 360 degrees?
Replace sin2x with the equivalent (1 - cos2x). Simplify, and use the quadratic equation, to solve for cos x.Replace sin2x with the equivalent (1 - cos2x). Simplify, and use the quadratic equation, to solve for cos x.Replace sin2x with the equivalent (1 - cos2x). Simplify, and use the quadratic equation, to solve for cos x.Replace sin2x with the equivalent (1 - cos2x). Simplify, and use the quadratic equation, to solve for cos x.
How do you solve the equation negative 3 cos t equals 1 in the interval from 0 to 2 pi?
Isolate cos (t): cos(t)=1/3. Use a calculator from here because the answer is not an integer or a simple number.
How do you solve theta if cos squared theta equals 1 and 0 is less than or equal to theta which is less than 2pi?
cos2(theta) = 1 so cos(theta) = ±1 cos(theta) = -1 => theta = pi cos(theta) = 1 => theta = 0
