Proving the tangent of the unit circle is given by the equation $z+a^2\overline{z}= 2a$
95473
Complex Numbers Geometry
60811
How to find the equation of a line, tangent to a circle, that passes through a given external point
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
119628
Proving an identity relating to the complex modulus: $z\bar{a}+\bar{z}a \leq 2|a||z|$
61641
Equations of lines tangent to an ellipse
57191
Show that if $a>e$, the equation $az^n=e^z$ admit $n$ roots in the unit disk - Rouché theorem
37985
Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
35244
Prove $\sin^2\theta + \cos^2\theta = 1$
139051
Pell type equation: $x^2-py^2=a$
77470
Find modulus of $\frac{|z_1-z_2|}{|1-(z_1)(\overline{z_2})|}$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
148233
Proof that every circle has the ratio of $\pi$
78712
Prove that $\frac{1}{\sin^2 z } = \sum\limits_{n= -\infty} ^ {+\infty} \frac{1}{(z-\pi n)^2} $
64497
prove that $\tan(\alpha+\beta) = 2ac/(a^2-c^2)$
82758
To prove $ \tan(A) + 2 \tan(2A) +4\tan4A + 8 \cot8A =\cot(A) $
133264
Constructing a circle through a given point, tangent to a given line, and tangent to a given circle
15287
Proving that second derivative is perpendicular to curve