How to prove $1+\cos2\theta+\cos4\theta+\cos6\theta+\cos8\theta=\frac{(\cos4\theta)(\sin5\theta)}{\sin\theta} $?
71413
Proving complex series $1 + \cos\theta + \cos2\theta +... + \cos n\theta $
106355
How to prove Lagrange trigonometric identity
72377
Show that $\sum_{n=1}^\infty r^n\cos(n\theta)=\dfrac{r\cos\theta -r^2}{1-2r\cos\theta+r^2}$ whenever $0<r<1$.
21826
How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$
90226
Proving trigonometric equation $\cos(36^\circ) - \cos(72^\circ) = 1/2$
9986
Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
33791
Is it generally true that $\arcsin \theta + \arccos \theta = \frac{\pi}{2}$?
114031
Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
120953
Show that, $2\arctan\left(\frac{1}{3}\right)+2\arcsin\left(\frac{1}{5\sqrt2}\right)-\arctan\left(\frac{1}{7}\right)=\frac{\pi}{4}$
100895
Prove $1 + \cos 2C - \cos 2A - \cos 2B = 4\sin A\sin B\cos C$ for $A$, $B$, $C$ the angles of a triangle
33905
Prove the following trigonometric identity: $\frac{\tan A+\sec A-1}{\tan A-\sec A+1}=\frac{1+\sin A}{\cos A}$
7296
Prove $(1-\cos x)/\sin x = \tan x/2$
148207
Express $\cos 6\theta $ in terms of $\cos \theta$
156162
Are $\cos^2 \theta$ and $\cos \theta^2$ the same?
52311
Prove that $0 \le \frac{1+\cos\theta}{2+\sin\theta} \le \frac{4}{3}$ for all real $\theta$.
56934
How do we prove $\cos(\pi/5) - \cos(2\pi/5) = 0.5$ ?.
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction