Prove $\sin(\cos x) \neq \cos(\sin x)$
2648
Show that the equation $\cos(\sin x)=\sin(\cos x)$ has no real solutions.
21941
Proving: $x = a_0 + \sum_{n=1}^{\infty}(a_n \cos nx + b_n \sin nx)$
11744
Maximum and minimum of $f(x)=\cos(\sin(x))-\sin(\cos(x))$
116580
Prove by induction: $\sin{x}+\sin{3x}+\dots+\sin{(2n-1)x}=\frac{\sin^2{nx}}{\sin{x}}$
87934
Deducing $\sin x + \cos x \ge 1$ from $(\sin x + \cos x)^2 = 1 + 2 \sin x \cos x$
6465
How to prove periodicity of $\sin(x)$ or $\cos(x)$ starting from the Taylor series expansion?
118687
Prove an inequality with a $\sin$ function: $\sin(x) > \frac2\pi x$ for $0<x<\frac\pi2$
138575
Proof that $\cos^2(x)\cosh^2(y) + \sin^2(x)\sinh^2(y) = -1 + \sin^2(x) - \sinh^2(y)$
29370
Trig integral $\int ( \cos{x} + \sin{x}\cos{x}) \, dx $
127380
Use vectors to prove $\cos(\beta - \alpha) = \cos \alpha \cos\beta + \sin\alpha \sin\beta$
49054
Show that $\left | \sin a - \sin b \right | \leq \left | a-b \right |$
17769
Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$
148632
How to expand $\cos nx$ with $\cos x$?
77130
How to prove this inequality $\left|x\sin{\frac{1}{x}}-y\sin{\frac{1}{y}}\right|<2\sqrt{|x-y|}$?
143050
If $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$,then prove that $\sin y=\frac{\sin x(3+\sin^2 x)}{(1+3\sin^2 x)}$
44438
Prove : $\frac{\cos(x_1) +\cos(x_2) +\cdots+\cos(x_{10})}{\sin(x_1) +\sin(x_2) +\cdots+\sin(x_{10})} \ge 3$
11711
Prove trigonometry identity for $\cos A+\cos B+\cos C$