If $cos(A-B)+cos(B-C)+cos(C-A)=\frac {-3}{2}$, prove that $cosA+cosB+cosC=sinA+sinB+sinC=0$
64255
Trigonometry problem
16270
Trigonometry question: $\sin^2(A) + \sin^2(B) - \sin^2(C) = 2\sin(A)\sin(B)\cos(C).$
51729
Solve the following equation: $\sqrt {\sin x - \sqrt {\cos x + \sin x} } = \cos x$
98745
To prove $(\sin\theta + \csc\theta)^2 + (\cos\theta +\sec\theta)^2 \ge 9$
57750
Solve identity: $\frac {\sin x}{1-\cos x} = \frac {1+\cos x}{\sin x}$
56166
Prove that $\frac{a}{b+2c+3d}+\frac{b}{c+2d+3a}+\frac{c}{d+2a+3b}+\frac{d}{a+2b+3c} \geq \frac{2}{3}.$
131688
Solve $\sin 7x+\sin 3x=0$
54175
Prove the trigonometric identity $\sin^4{x} = \frac{3-4\cos{2x}+\cos{4x}}{8}$
111847
For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$
14386
Proof of an equality involving cosine $\sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + \sqrt{2}}}}\ =\ 2\cos (\pi/2^{n+1})$
12414
prove that : $\cos x \cdot \cos(x-60^{\circ}) \cdot \cos(x+60^{\circ})= \frac14 \cos3x$
108245
Solving the complex equation $\sin(z) = \cos(z)$
142610
Solving $\sin x\cos3x+\cos x\sin3x=\sqrt{3}/2$ in the interval $[0,2\pi]$
56934
How do we prove $\cos(\pi/5) - \cos(2\pi/5) = 0.5$ ?.
123136
Proof of the identity: $c\sin \frac{A-B}{2} \equiv (a-b) \cos \frac{C}{2}$
59014
Prove that $\sin(2A)+\sin(2B)+\sin(2C)=4\sin(A)\sin(B)\sin(C)$ when $A,B,C$ are angles of a triangle
17264
Given $a,b,c$ are the sides of a triangle. Prove that $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$