If $x=2\pi/2009$, then evaluate $\cos x \cos 2x \cos 3x \cdots \cos 1004x$
59003
Product of cosines: $ \prod_{r=1}^{7} \cos \left(\frac{r\pi}{15}\right) $
119669
Evaluate $\int \frac{1}{\sin x\cos x} dx $
129913
Evaluate: $I=\int\limits_{0}^{\frac{\pi}{2}}\ln\frac{(1+\sin x)^{1+\cos x}}{1+\cos x}dx$
55738
Evaluating $\int _0^{\frac{\pi }{2}}\:\frac{\sqrt[3]{\sin^2\left(x\right)}}{\sqrt[3]{\sin^2\left(x\right)}+\sqrt[3]{\cos^2\left(x\right)}}dx$
106441
Find the value of $\binom{2000}{2} + \binom{2000}{5} + \binom{2000}{8} + \cdots \binom{2000}{2000}$
17769
Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$
36586
Evaluating $\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta$
121071
Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$
107142
If $(x_n) \to x$ then $(\sqrt[n]{x_1x_2\cdots x_n}) \to x$
29322
Evaluate $\int_{0}^{\frac{\pi}{2}} \frac{\sin^2 nx}{\sin x} \text{d}x$
142610
Solving $\sin x\cos3x+\cos x\sin3x=\sqrt{3}/2$ in the interval $[0,2\pi]$
130058
Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
27790
Evaluating $\int_0^{\large\frac{\pi}{4}} \log\left( \cos x\right) \, \mathrm{d}x $
18546
Geometric intuition for $\pi /4 = 1 - 1/3 + 1/5 - \cdots$?
138230
Evaluate $ \int^{\frac{\pi}{2}}_0 \frac{\sin x}{\sin x+\cos x}\,dx $ using substitution $t=\frac{\pi}{2}-x$
48586
Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
106544
Solve $ \frac{2}{\pi}\int_{-\pi}^\pi\frac{\sin\frac{9x}{2}}{\sin\frac{x}{2}}dx $