Given $x, y$ are acute angles such that $\sin y= 3\cos(x+y)\sin x$. Find the maximum value of $\tan y$.
73512
Trigonometry Olympiad Question
114844
Global maxima/minima of $f(x,y,z) = x+y+z$ in $A$
61343
Prove that if $\alpha, \beta, \gamma$ are angles in triangle, then $(tan(\frac{\alpha}{2}))^2+(tan(\frac{\beta}{2}))^2+(tan(\frac{\gamma}{2}))^2\geq1$
44715
Exact value for $\cos 36°$
116223
Show that the angles satisfy $x+y=z$
617
Find θ: $β=\arctan\frac{(R+r)·\sin(θ)-r·\sin(θ(1+\frac{R}{r}))}{(R+r)·\cos(θ)-r·\cos(θ(1+\frac{R}{r}))}$
145559
Trigonometry problem on product of trig functions.
31257
Let $a,b,c>0$ such that $a+b+c=3$, find max/min of $\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}$
11744
Maximum and minimum of $f(x)=\cos(\sin(x))-\sin(\cos(x))$
143050
If $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$,then prove that $\sin y=\frac{\sin x(3+\sin^2 x)}{(1+3\sin^2 x)}$
123920
How prove this inequality $\tan{(\sin{x})}>\sin{(\tan{x})}$
103218
Find $\lim_{(x,y) \to (0,0)} \frac{\tan(x^3+y^3)}{\sin(x^2+y^2)}$
45227
If $\sin \theta+\cos\theta+\tan\theta+\cot\theta+\sec\theta+\csc\theta=7$, then $\sin 2\theta$ is a root of $x^2 -44x +36=0$ My own bonafide attempt.
12014
Solving a multi-variable trig sum to find the max separation btwn 2 ellipses
12646
In acute angle triangle, prove that $\cos (A-B) \cos (B-C) \cos (C-A)\ge 8\cos A \cos B \cos C$
46665
Solving $\cos x+\sin x-1=0$
12841
Ratio of sines given, find ratio of cosines?