query: How do I prove: $\cos (\theta + 90^\circ) \equiv - \sin \theta $
positive_passages.docid: 149447
positive_passages.text: Proving $\sin (x)=\cos (90^\circ-x)$
negative_passages.docid: 45619
negative_passages.text: Prove: $|a\sin x+b \cos x|\leq \sqrt{a^2+b^2}$
negative_passages.docid: 1859
negative_passages.text: Proving $\arctan(\sqrt{x^2+1}-x)=\frac{\pi}{4}-\frac{1}{2}\arctan(x)$
negative_passages.docid: 100320
negative_passages.text: Prove that $\cos\frac {2\pi}{7}+ \cos\frac {4\pi}{7}+ \cos\frac {8\pi}{7}=-\frac{1}{2}$
negative_passages.docid: 104321
negative_passages.text: Prove that $1 + \cos\alpha + \cos\beta + \cos\gamma = 0$
negative_passages.docid: 114031
negative_passages.text: Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
negative_passages.docid: 147684
negative_passages.text: Prove that $\sin \theta=\frac{3 \sin \alpha+\sin^3 \alpha}{1+3\sin^2 \alpha}$ using given condition
negative_passages.docid: 103536
negative_passages.text: How to prove $|e^{i\theta} - 1| \leq |\theta|$?
negative_passages.docid: 37985
negative_passages.text: Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
negative_passages.docid: 143072
negative_passages.text: Proving $|\sin x - \sin y| < |x - y|$
negative_passages.docid: 135543
negative_passages.text: Proof of Angles going beyond 90 degrees in Trigonometry
negative_passages.docid: 107067
negative_passages.text: Finding the argument of $z=1-\cos(2\theta)-i\sin(2\theta)$
negative_passages.docid: 98745
negative_passages.text: To prove $(\sin\theta + \csc\theta)^2 + (\cos\theta +\sec\theta)^2 \ge 9$
negative_passages.docid: 35244
negative_passages.text: Prove $\sin^2\theta + \cos^2\theta = 1$
negative_passages.docid: 71413
negative_passages.text: Proving complex series $1 + \cos\theta + \cos2\theta +... + \cos n\theta $
negative_passages.docid: 44391
negative_passages.text: How can I prove $n - 2\sqrt{n} = \Theta(n)$
negative_passages.docid: 7296
negative_passages.text: Prove $(1-\cos x)/\sin x = \tan x/2$