Trigonometric F...

If $$cos \alpha + cos \beta = a , \, sin \alpha + sin \beta = b \, and \, \alpha - \beta  = 2 \theta \, then \, \dfrac{cos \, 3 \theta }{cos \, \theta}$$ =

If $$a$$, $$b$$, $$c$$, $$t$$ are the solution of the equation $$\tan\left(\theta+\dfrac{\pi}{4}\right)=3\ tan 3\theta$$, no two of which have equal tangents . Then, the value of $$\tan a+\tan b+\tan c+\tan t=$$

If $$\alpha$$ is a root of $$25\cos^2\theta +5\cos\theta -12=0, \dfrac{\pi}{2} < \alpha < \pi$$, then $$\sin 2θ $$ is equal to?

The value of $$\sin {27^ \circ } - \cos {27^ \circ }$$ is equal to 

The value of $${\cos ^2}{73^ \circ } + {\cos ^2}{47^ \circ } - {\sin ^2}{43^ \circ } + {\sin ^2}{107^ \circ }$$ is equal to :

If $$\tan \theta  + \tan 4\theta  + \tan 7 = \tan \theta \tan 4\theta \tan 7\theta ,\,\,then\,\,\theta  = $$

If $$\tan \theta + \sec \theta = \sqrt{3}$$, then the principal value of $$\left(\theta + \dfrac{\pi}{6}\right)$$ is

If $$4\ \sin^{2}x-1=0$$ and $$0 < x < 2 \pi$$, then positive values of $$x$$ are 

If $$\sin { x } sin{ \left( { 60 }^{ O }+x \right) .\left( { 60 }^{ O }-x \right)  }=\frac { 1 }{ 8 } $$ then$$x=$$