query: Concept of Trigonometric identities
positive_passages.docid: 77978
positive_passages.text: Show that $\frac {\sin x} {\cos 3x} + \frac {\sin 3x} {\cos 9x} + \frac {\sin 9x} {\cos 27x} = \frac 12 (\tan 27x - \tan x)$
negative_passages.docid: 141645
negative_passages.text: Trigonometric series sum proof
negative_passages.docid: 67172
negative_passages.text: What's the intuition behind the identities $\cos(z)= \cosh(iz)$ and $\sin(z)=-i\sinh(iz)$?
negative_passages.docid: 122705
negative_passages.text: Solution of trigonometric equation $0 = x\cos(x)+2$
negative_passages.docid: 140140
negative_passages.text: An identity which applies to all of the natural numbers
negative_passages.docid: 59014
negative_passages.text: Prove that $\sin(2A)+\sin(2B)+\sin(2C)=4\sin(A)\sin(B)\sin(C)$ when $A,B,C$ are angles of a triangle
negative_passages.docid: 137376
negative_passages.text: Proving a trig identity: $\frac{\sin(A + B)}{\sin(A - B)}=\frac{\tan A + \tan B}{\tan A - \tan B}$
negative_passages.docid: 27513
negative_passages.text: Trigonometric bounds
negative_passages.docid: 104427
negative_passages.text: Sines and cosines of angles in arithmetic progression
negative_passages.docid: 118586
negative_passages.text: Confused About Trigonometric Substitution
negative_passages.docid: 13297
negative_passages.text: Prove the following trigonometric identity without a calculator involved
negative_passages.docid: 83981
negative_passages.text: How to prove those "curious identities"?
negative_passages.docid: 96367
negative_passages.text: Intuition of Addition Formula for Sine and Cosine
negative_passages.docid: 118577
negative_passages.text: Fallacious proof involving trigonometry
negative_passages.docid: 6465
negative_passages.text: How to prove periodicity of $\sin(x)$ or $\cos(x)$ starting from the Taylor series expansion?
negative_passages.docid: 44119
negative_passages.text: Prove that $\cos (A + B)\cos (A - B) = {\cos ^2}A - {\sin ^2}B$
negative_passages.docid: 67988
negative_passages.text: Trigonometric curiosity