Trigonometric F...

The least value of a for which the expression $$f(x)=\cfrac{4}{\sin x}+\cfrac{1}{1-\sin x}=a^{2}$$ has at least one solution on the interval $$(0,\quad \pi /2)$$ is 

If $$\sin \theta +\cos \theta =1$$, then the value of $$\sin 2\theta$$ is equal to:

If  x=$$\frac{{2\left( {\sin {1^o} + \sin {2^o} + \sin {3^o} + .... + \sin {{89}^o}} \right)}}{{2\left( {\cos {1^o} + \cos {2^o} + ..... + \cos {{44}^o}} \right) + 1}}$$, then the value of $${\log _x}2$$ is equal 

The number of solution of $$\sin 3x=\cos 2x$$ in the interval $$\left(\dfrac{\pi}{2},\pi\right)$$ is :

The solution set of the equation $$4 \sin \theta-2 \cos \theta-2\sqrt {3} \sin \theta+\sqrt {3}=0$$ in the interval $$(0,2\pi)$$ is-

Find the principal solution of the following equation:
$$\tan { x=\sqrt { 3 }  } $$

The number of real solutions $$x$$ of the equation $$\cos ^ { 2 } ( x \sin ( 2 x ) ) + \frac { 1 } { 1 + x ^ { 2 } } - \cos ^ { 2 } x + \sec ^ { 2 } x$$ is

 $$\dfrac{\cos A}{1- \sin A}$$=

Total number of solutions of $$\sin^{2}x-\sin x-1=0$$ in $$[-2\pi, 2\pi]$$ is equal to:

The solution set of equation
$$4\sin{\theta}\cos{\theta}-2\cos{\theta}-2\sqrt{3}\sin{\theta}+\sqrt{3}=0$$ in the interval $$(0, 2\pi)$$