# What is identities: Definition and 422 Discussions

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle.
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

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1. ### A Identity with Gamma matrices and four-vector contractions

Is the fowwowin identity correct for a generic four-vector"q"? What is the proof? Thank you.
2. ### Geometry Looking for a good book about trigonometry

Hi all! I've never been studied the identities and such of secant, cosecant and cotangent. Yet I think, it would be useful to have them in my toolbox. Thus I'm asking, if anyone would know a reasonable book or other kind of material (paper or pdf) about trigonometry that has brief theory...
3. ### Another way to find trig identities

Using the identity's (1) (2) Gives, Why dose this elegant method work? Many thanks!
4. ### Proving trig identities -- Is the method related to the unit circle?

Why when proving trig identities, Do we assume that r = 1 from ## rcis\theta = r[\cos\theta + i\sin\theta]##? This makes me think that this is somehow it is related the unit circle. Note: I am trying to prove the ##cos3\theta## identity and am curious why we assume that the modulus is 1...
5. ### Proof of the trig identities for half-angles

I was just checking this out the sin##\frac {A}{2}## property, in doing so i picked a Right-Angled triangle, say ##ABC##, with ##AB=5cm##, ##BC=4cm## and ##CA= 3cm##. From this i have, ##s=6cm## now substituting this into the formula, ##sin\frac {A}{2}##= ##\frac {1×3}{5×3}##=##\frac...
6. ### MHB Can you prove the following two difficult trigonometric identities?

Can you prove the following? [sec(x)]^6 - [tan(x)]^6 = 1 + 3*[tan(x)]^2*[sec(x)]^2 [sin(x)]^2*tan(x) + [cos(x)]^2*cot(x) + 2*sin(x)*cos(x) = tan(x) + cot(x) If not, the following free math tutoring video shows you the method:
7. ### MHB Problems involving Trigonometric Identities

What are the step-by-step in solving these problems?
8. ### Proving trigonometry identities

I was just looking at the problem below: there may be several ways to prove the identity: question: Mark scheme solution: My take: we may also use ##sin^{2}x+cos^{2}x≡(sin x+ cos x)(sin x-cosx)##... we end up with(##\frac 2 {\sqrt{2}}##cos ∅)(##\frac 2...
9. ### 4cos(2x) = 8sin(x)cos(x) -- Help with identities

4cos2x = 8sinxcosx 4cos2x - 8sinxcosx = 0 Now I am stuck. I don't know what identities to use. I can see it was set to 0 for a reason. But why? I know the answer is 4 - 4tan2x = 0 but how? Thanks.
10. F

### How to approach vector calculus identities?

Majoring in electrical engineering imply studying Griffiths book on electrodynamics, so I have begun reading its first chapter, which is a review of vector calculus. A list of vector calculus identities is given, and I would like to derive each one, with one of them being ##\nabla \cdot (A...
11. ### MHB Solve Situational Problems Involving Trigonometric Identities

Hi! I am so confused about the given and what is being asked, I don't know how to solve it. This topic is solving situational problems involving trigonometric identities. Your help would be a big one for me :) Thank you so much in advance!
12. ### B Verifying trig identities.... what about when tan is undefined?

Hello, If I wanted to verify tan(x)cos(x) = sin(x), what about when x is pi/2? LHS has a restricted domain so it can't equal sin(x). Does this equation only work with a restricted domain? Nothing in my textbook discusses that. Thank you

20. ### Trigonometry - Double Angle Identities

Homework Statement If I have the following relation: tan(2x) = (B/2) / (A - C) but tan(2x) = sin(2x) / cos(2x) How do I obtain an expression for sin(x) and cos(x) in terms of the constants, B,A,C only? Homework Equations cos(2x) = 1- 2 sin^2(x) The Attempt at a Solution [/B] I can't...
21. ### Proving Trigonometric Identities: (sin φ+1-cos φ)/(sin φ+cos φ-1)

Homework Statement Show that ## {(tan φ+sec φ-1)/(tan φ-sec φ+1)}≡ {(1+sin φ)/cos φ}##[/B]Homework EquationsThe Attempt at a Solution ## (sin φ+1-cos φ)/(sin φ+cos φ-1)##[/B]
22. ### MHB How to Prove a Trigonometric Identity Involving x, y, and z?

If xy+yz+zx=1 then prove (x^2-1)(y^2-1)/xy+(y^2-1)(z^2-1)/yz+(z^2-1)(x^2-1)/zx=4 with trigonometric identities such as cotAcotB+cotBcotC+cotCcotA=1
23. ### MHB Proving Identities Using Axioms of Equality

Given the following axioms: For all A,B,C...we have: 1) A=A 2) A=B <=> B=A 3) A=B & B=C => A=C 4) A=B => A+C= B+C 5) A=B=> AC =BC ( NOTE :Instead of writing A.C or B.C e.t.c we write AB.BC e.t.c) 6) A+B= B+A..........AB=BA 7) A+(B+C) = (A+B)+C............A(BC)=(AB)C 10)...
24. ### I Superposition of particle identities

Suppose a neutral meson decays into an electron and a positron. Are the two particles entangled as they fly apart? Before any measurement takes place, are the particles in a mixed superposition as to which one is the electron, and which one is the positron? Is there a way to test for such...
25. ### Trig Identities -- example problem confusion

Homework Statement Back with more trig identities. Verify that the following is an identity ##-tan\frac{a}{2} = cot\left(a\right)-csc\left(a\right)## Homework Equations All pythagorean identities, double angle formulas, half angle formulas The Attempt at a Solution In the picture that I've...
26. ### How Do You Simplify Trigonometric Expressions Using Basic Identities?

Homework Statement Express (1+cot^2 x) / (cot^2 x) in terms of sinx and/or cosx Homework Equations cot(x) = 1/tan(x) sin^2(x) + cos^2(x) = 1 The Attempt at a Solution I do not know if I am solving this problem correctly. Is there an easier route than the way I have solved it, if it is solved...
27. ### How to prove vector identities WITHOUT using levi civita ?

Mentor note: Thread moved from homework sections as being a better fit in the math technical section. Multiplying components of both sides are also off limits. I am trying to derive vector identities on introduction chapters in various EMT books. For example : (AXB).(CXD) = (A.C)(B.D) -...
28. ### B Eliminating Variables in Trigonometric Equations for Research Purposes

Consider the following set of equations: ##r = \cosh\rho \cos\tau + \sinh\rho \cos\varphi## ##rt = \cosh\rho \sin\tau## ##rl\phi = \sinh\rho \sin\varphi## Is there some way to combine the equations to get rid of ##\varphi## and ##\tau## and express ##\rho## in terms of ##r, t, \phi##? I...

40. ### Proving Reciprocal Identities: (secx+1)/(sin2x) = (tanx)/2cosx-2cos2x

Homework Statement (secx+1)/(sin2x) = (tanx)/2cosx-2cos2x) Homework EquationsThe Attempt at a Solution Left Side ((1+cosx)/cosx)/2sinxcosx ((1+cosx)/cosx) x (1/2sinxcosx) cancel the a cosx from both to get (1/2sinxcosx) This is all I could manage with left side so I tried right side Right...

42. ### MHB How can you solve equations involving trigonometric identities?

Can anybody please help me solve either of these equations Solve the following equation for angles between 0 and 360 degrees 4cos²θ + 5sinθ = 3 4cot² - 6 cosec x = -6
43. ### B Factoring quadratic equation (with trig identities used)

Is it possible to factor a quadratic equation along the lines of asin^2x -bsin2x+c ? If so, how? The sin2x seems to be a problem since when expanded it becomes 2sinxcosx, but I'm wondering if it is possible, and how it would be done? Thanks in advance.
44. ### Trig identities (I think?) for precalc review

Homework Statement My calc class is having me review precalc(which I'm really rusty on...) 21. Find sin θ, sec θ, and cot θ if tan θ = 27 22. Find sin θ, cos θ, and sec θ if cot θ = 4. 23. Find cos 2θ if sin θ = 15 24. Find sin 2θ and cos 2θ if tan θ = √2 25. Find cos θ and tan θ if sin θ =...
45. ### Is My Trigonometric Identity Proof Correct?

Homework Statement Homework Equations none The Attempt at a Solution [/B] I literally just posted this in the thread: https://www.physicsforums.com/threads/proving-identities.881951/ But since it was marked solved I doubt anyone will see it. So sorry in advance for making a new thread on...
46. ### How Do You Prove Trigonometric Identities with Minimal Equations?

Homework Statement prove the following identity [/B] Homework Equations no equations required The Attempt at a Solution I've been trying to prove this identity, but no matter what I do, I can't seem to make both sides the same here is my answer to this qts so far: can someone please tell me...
47. ### I Question ,trigonometric identities equation and functions ?

what is the difference between trigonometric identities , equations and functions ...? is it possible to apply some numerical method on a trigonometric function ?? i was looking for an example where numerical methods could be applied on a trigonometric function ... i am not sure what you...
48. ### A Difficulty in understanding contracted Bianchi identities

I am confused about the contraction in the proof of the contracted Bianchi identities in https://en.wikipedia.org/wiki/Proofs_involving_covariant_derivatives from the step {g^{bn}}(R_{bmn;l}^m - R_{bml;n}^m + R_{bnl;m}^m) = 0 it seems that the following two quantities are equal...
49. ### Why Does This Trigonometric Identity Seem Incorrect?

Homework Statement sin^2x + 4sinx +4 / sinx + 2 = sinx +2 Homework EquationsThe Attempt at a Solution L.S = sin^2x + 4sinx +4 / sinx + 2 =1-cos^2+4(sinx + 1) / sinx +2 Not sure where to go from there. Not sure if I was even supposed to factor out the 4?
50. ### Vector identities in quantum mechanics

The overall problem is to prove that [L^2,[L^2,\hat{r}]]=2\hbar^2 {L^2,r} I feel I am very close to solving this problem but I need a quantum version of the vector identity ax(bxc). Because the relevant vectors are operators that don't commute, there is a problem. Does anybody know of a source...