If \( \, \tan A = \dfrac{1 - \cos B}{\sin B} \, \) then \( \, \tan 2A = \tan B \, \).
True
The equality \( \, \sin A + \sin 2A + \sin 3A = 3 \, \) holds for some real value of \(A\).
False
\( \, \sin 10^\circ \, \) is greater than \( \, \cos 10^\circ \, \).
False
\( \cos \dfrac{2\pi}{15} \, \cos \dfrac{4\pi}{15} \, \cos \dfrac{8\pi}{15} \, \cos \dfrac{16\pi}{15} = \dfrac{1}{16} \).
True
One value of \(\theta\) which satisfies the equation \( \, \sin^4 \theta - 2 \sin^2 \theta - 1 \, \) lies between \(0\) and \(2\pi\).
False
If \( \, \csc x = 1 + \cot x \, \) then \( x = 2n\pi \) or \( x = 2n\pi + \dfrac{\pi}{2} \).
True
If \( \, \tan \theta + \tan 2\theta + \sqrt{3} \, \tan \theta \, \tan 2\theta = \sqrt{3} \, \), then \( \, \theta = \dfrac{n\pi}{3} + \dfrac{\pi}{9} \, \).
True
If \( \, \tan(\pi \cos \theta) = \cot(\pi \sin \theta) \, \) then \( \, \theta - \dfrac{\pi}{4} = \pm \dfrac{1}{2\sqrt{2}} \, \).
True