Better proof for $\frac{1+\cos x + \sin x}{1 - \cos x + \sin x} \equiv \frac{1+\cos x}{\sin x}$
10289
Need help in proving that $\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac 1{\sec\theta - \tan\theta}$
116580
Prove by induction: $\sin{x}+\sin{3x}+\dots+\sin{(2n-1)x}=\frac{\sin^2{nx}}{\sin{x}}$
19896
Prove $\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\geq \frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}$
146594
Prove that $\frac{d}{dx}(\tan^{-1}(x))=\frac{1}{1+x^2}dx$
48824
Prove: $ \frac{1}{\sin 2x} + \frac{1}{\sin 4x } + \cdots + \frac{1 }{\sin 2^n x} = \cot x - \cot 2^n x $
53307
how to strictly prove $\sin x<x$ for $0<x<\frac{\pi}{2}$
51979
Is there a geometrical method to prove $x<\frac{\sin x +\tan x}{2}$?
58633
Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$
25054
Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction
33097
Proving an inequality without an integral: $\frac {1}{x+1}\leq \ln (1+x)- \ln (x) \leq \frac {1}{x}$
57750
Solve identity: $\frac {\sin x}{1-\cos x} = \frac {1+\cos x}{\sin x}$
24656
Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
71299
Prove that $\frac{a}{b} < \frac{a+c}{b+d} <\frac{ c}{d}$
58041
Prove by Mean Value Theorem $\frac{x}{1+x}0$
112565
Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{9}{a+b+c} : (a, b, c) > 0$
48586
Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
102334
How can you prove $\frac{n(n+1)(2n+1)}{6}+(n+1)^2= \frac{(n+1)(n+2)(2n+3)}{6}$ without much effort?