Trigonometric F...

 $$\displaystyle \frac{\sin(\theta+A)}{\sin(\theta+B)}=\sqrt{\frac{\sin 2A}{\sin 2B}}$$ then $$\tan^{2}\theta=$$ 

lf $$\alpha$$ and $$\beta$$ are two different solutions lying between $$\displaystyle \frac{-\pi}{2}$$ and $$\displaystyle \frac{\pi}{2}$$ of the equation $$2t\mathrm{a}n\theta+\mathrm{S}\mathrm{e}\mathrm{c}\theta=2$$ then $$ t\mathrm{a}n\alpha+t\mathrm{a}n\beta$$ 

If $$\displaystyle \frac{\cos(A+B)}{\cos(A-B)}+\frac{\cos(C-D)}{\cos(C+D)}=0$$, then $$\cot A\ cot B\cot C\, cot D$$ is equal to 

If $$y\displaystyle \tan\left (\theta-\dfrac {\pi}{6}\right ) = x\tan \left (\theta + \dfrac {2\pi}{3}\right ) $$ , then $$\dfrac {y+x}{y-x}=$$

$$\cos\alpha\sin(\beta-\gamma)+\cos\beta\sin(\gamma-\alpha)+\cos\gamma\sin(\alpha-\beta)= $$

$$\displaystyle \sum \cos \alpha \sin (\beta - \gamma) =$$

 $$\sin A+\sin B=\sqrt{3}(\cos B-\cos A)$$. Find the value of $$\sin 3A+\sin 3B$$

 If $$\displaystyle \tan A=\cfrac{x\sin B}{1-x\cos B}$$
and $$\displaystyle \tan B=\cfrac{y\sin A}{1-y\cos A}$$, then $$\displaystyle \cfrac{\sin A}{\sin B}=$$

If $$\displaystyle \sin x\cos y=\frac{1}{4},3\tan x=4\tan y$$, then $$ \sin(x-y)=$$

For all values of $$\theta,\cos\theta.\text{cosec }\theta\sqrt{\sec^2\theta-1}$$ is