Trigonometric F...

Genral solution of the equation $$\theta -cosec\theta =\dfrac { 4 }{ 3 }$$ is :

If $$\sin \alpha = a \sin \beta$$ and $$\cos \alpha = b \cos \beta$$ then $$\tan \alpha =$$

If $$\tan \theta +\sec \theta =\sqrt {3}, 0< \theta < \pi$$ then $$\theta $$ is equal to

If $$\cosh x=\sec \theta$$, then $$\coth^{2}(x/2)=$$

Choose the correct answer the following:
2) The principle solution of $$\sec{x}+2=0$$ is____

$$\tan\left(\dfrac{\pi}{4}+x\right)+\tan\left(\dfrac{\pi}{4}-x\right)=2$$, then $$x=$$

One of principal solution of $$\sqrt 3 \sec x =  - 2$$ is equal to

If $$\alpha +\beta =\dfrac { 5\pi  }{ 4 } $$, then value of $$\dfrac { \cot { \alpha  } \cdot\cot { \beta  }  }{ \left( 1+\cot { \alpha  }  \right) \left( 1+\cot { \beta  }  \right)  }$$ is (wherever defined)-

$$cos[tan^{-1}(sin(cot^{-1}x))]$$ is equal to-

If $$sin A=\dfrac{3}{5},\tan B=\dfrac{1}{2}$$ and $$\dfrac{\pi}{2}<A<\pi<B<\dfrac{3\pi}{2}$$, then the value of $$8\tan A-\sqrt{5}sec B=$$