1. hyperbola

    Trig Identity

    I've reached the 'Trig Identity' section of my calculus textbook. I'm given this problem. 4\sin^2x + 7\cos^2x = 4 + 3\cos^2x I can see a trig the identity \sin^2x + \cos^2x = 1 \frac{4\sin^2x + 7\cos^2x} {\sin^2x} = 4 + 3\cos^2x 4 + \frac {7\cos^2x} {\sin^2x} = 4 + 3\cos^2x and that's as...
  2. U

    Identity rule

    Hi. Im working on marices and i am working on showing \((A^{-1}A)X=A^{-1}(AX)\) without using associative propety law. I have \((A^{-1}A)X\) done and im up to the last steps on \(A^{-1}(AX)\). The final matrix vector is \(\begin{pmatrix} x \\\ y \end{pmatrix}\) The final part i need to...
  3. B

    basic trig identity

    sec^2(pi/4).i dont know how to calculate since we need to convert that power 2 to 1.we have equivalent trigonometric identies for cos^2 and Sin^2 but we dont have for sec^ i would i calculate that?
  4. G

    How do I prove this seemingly simple trigonometric identity

    a=\sinθ+\sinϕ b=\tanθ+\tanϕ c=\secθ+\secϕ Show that, 8bc=a[4b^2 + (b^2-c^2)^2] I tried to solve this for hours and have gotten nowhere. Here's what I've got so far: \\a= 2\sin(\frac{\theta+\phi}{2})\cos(\frac{\theta-\phi}{2}) \\ b = \frac{2\sin(\theta+\phi)}{\cos(\theta+\phi)+...
  5. V

    prove Summation identity

    Hello! I got stucked in this problem, I don't know how I should proceed with this problem, I'm supposed to prove that the first summation true is, and to get the result of the second one by contracting the terms. Thank you very much in advance!!! :spin:
  6. J

    Integral with trig identity (help)

    \int \sqrt{40+6x-x^2}dx So I solved it out and managed to get the answer using (x-3) = 7sin(theta) \frac{49}{2}(\theta+\frac{sin(2\theta)}{2})+C However, using the double angle identity, does the answer above equal: \frac{49}{2}(\theta+sin\theta cos\theta)+C I punched both...
  7. E

    ln of negative number with Euler's identity

    I've got a question which has been bugging me for a while, hoping you can help. Does ln(10)+ln(-1) = ln(10)-ln(-1) Because if you combine the ln terms, you get ln(-10) on both sides, but when you use Euler's formula, you get ln10 + iπ on one side and ln10 - iπ on the other. What's going on?
  8. N

    Pascal’s identity proof

    (1) In a game of chess, the Queen is allowed to move vertically, horizontally, or diagonally, in any direction, for any number of spaces. Try to place 8 Queens on a standard 8 x 8 chessboard so that none of the Queens is attacking any of the others (that is, no Queen can make one move and...
  9. S

    Curl vector identity proof

    Hi Can any help proving following identity (∇ x A) x A =(A.∇)A-1/2modulus(A^2)
  10. A

    Doubts from transposition, fixing and Identity

    Dear All, Please see the attachment for the text i will be referring to. what does "I = τ1 · · · τm, where each τj is a transposition acting on {1, . . . , n}. Clearly, m != 1, thus m ≥ 2. Suppose, for the moment, that τm does not fix n". what does fixing n mean...
  11. R

    Verify the following identity

    \sec \langle {y} \rangle + \tan \langle y \rangle = \frac {\cos \langle y \rangle }{1- \sin \langle y \rangle} I know you guys can verify this with ease, but I'm looking for how and why it's done the way you do it. Base knowledge please. Thank you, Roketmike
  12. C

    A question upon infinitesimals and Euler's Identity

    Hello I was recently shown a proof of Euler's Identity, one that was quite simple in my opinion. However there was a single part I didn't quite get concerning the use of dy/dx as a fraction. The proof is roughly as follows: Make a unit-circle in the complex plane, using polar coordinates. Any...
  13. M


    find tan(pi/7)tan(2pi/7)tan(3pi/7)
  14. raul21

    A Ramanujan identity 3

    1 + 9 (1/4)^4 + 17 ((1x5)/(4x8 ))^4 + 25 ((1x5x9)(4x8x12))^4 + etc. = (2sqrt2)/(sqrtpi {Gamma(3/4)}^2) Can someone prove this please?
  15. raul21

    A Ramanujan identity

    $1+9\frac{{1}{4}}^4+17\frac{{1x5}{4x8}}+25\frac{{1x5x9}{4x8x12}}$ + etc. = $\frac{{2\sqrt2}{\sqrt\pi{{\Gamma\frac{3}{4}}^2}}}$ Can someone prove this please?
  16. raul21

    A Ramanujan identity

    $1+9\frac{{1}{4}}^4+17\frac{{1x5}{4x8}}+25\frac{{1x5x9}{4x8x12}}$ + etc. = $\frac{{2\sqrt2}{\sqrt\pi{{\Gamma\frac{3}{4}}^2}}}$ Can someone prove this please?
  17. S

    Tangent Identity: Not Always True?

    Hi All, I have come across a dilemma regarding a problem: (tan(2a) - tan( 7a)) / (1 + tan(2a)*tan(7a)) = 1 where 0 <= a < 360 When I used the difference identity for tangent, I get this equation and solution(degrees): tan(5a) = -1 a = 27 + 36n where n is all real numbers. a is a set that...
  18. T

    NEED HELP proving trig identity!!

    Hey guys can anyone help me prove the following trig identity? Sec 2A (Cos^2 A- Sin^2 A) =1 Would greatly appreciate it!!
  19. D

    An identity

    Hello! For what values of a, b relationship 2x+3y=ax-by is an identity?
  20. W

    Trig Identity

    Is there a trig identity that would make this equality true? -x sin2xy = y cos2xy thanks for any help