Trigonometric F...

If $$(1+\tan{A}).(1+\tan{B})=2$$, then $$A+B$$ is 

If $$3\sin { 2\theta  } =2\sin { 3\theta  }$$ and $$0<\theta <\pi$$, then value of  $$\sin { \theta  }$$ is 

$${ cos }^{ 2 }2x+2{ cos }^{ 2 }x=1,x\epsilon \left( -\pi ,\pi  \right)$$, then $$x$$ can take the values

The number of solutions to the equation $$sin\ 5x+\ sin\ 3x\ +\ sin\ x=0$$ for $$\ 0\leq x\leq \pi$$ is

If $$\cos^{2}x=\sin x$$, then the value of $$\cos^{2}x(1+\cos^{2}x)$$ is equal to

If $$\cos2x\ +\ 2\cos\ x\ =\ 1$$, then $$\sin^{2}x(2-\cos^{2}x)$$ is

$$\dfrac{{\sec 8{\text{A}} - 1}}{{\sec 4{\text{A}} - 1}} = $$

If $$\tan \theta + \, \cot \theta = 4$$, then the value of $$\tan^3 \theta + \cot^3 \theta$$ is 

The positive integer value of $$n>3$$ satisfing the equation
 $$\frac{1}{{\sin \left( {\frac{\pi }{n}} \right)}} = \frac{1}{{\sin \left( {\frac{{2\pi }}{n}} \right)}} + \frac{1}{{\sin \left( {\frac{{3\pi }}{n}} \right)}}$$
 is