Introduction to...

Choose the correct option and justify your choice:
$$\displaystyle \sin { 2A } =2\sin { A } $$ is true when $$A =$$

Choose the correct option. Justify your choice.
$$\displaystyle \frac { 1+{ \tan }^{ 2 }A }{ 1+{ \cot }^{ 2 }A } =$$

Choose the correct option and justify your choice:
$$\displaystyle \frac { 1-{ \tan }^{ 2 }{ 45 }^{ \circ  } }{ 1+{ \tan }^{ 2 }{ 45 }^{ \circ  } } =$$

Choose the correct option and justify your choice:
$$\displaystyle \frac { 2\tan { { 30 }^{ \circ  } }  }{ 1+{ \tan }^{ 2 }{ 30 }^{ \circ  } } =$$

If $$\sin \theta \, + \, \cos \theta \, = \, p, \, \sin^{3} \, \theta \, + \, \cos^{3} \, \theta \, = \, q$$, then $$ p(p^{2} \, - \, 3) \, = \, $$  

If the area of $${\Delta}$$ $$ABC$$ is $$8\sqrt{3}$$ sq. units, then the length of $${AB}$$ is

$$\tan 10^{\circ} \tan 20^{\circ} \tan 30^{\circ} \tan 40^{\circ} \tan 50^{\circ} \tan 60^{\circ} \tan 70^{\circ} \tan 80^{\circ} $$ is equal to

If $$\displaystyle \sin { x } +{ \sin }^{ 2 }x=1$$, then $$\displaystyle { \cos }^{ 12 }x+3{ \cos }^{ 10 }x+3{ \cos }^{ 8 }x+{ \cos }^{ 6 }x$$ is equal to:

Simplify $$\sin^3\theta +\sin\theta -\sin\theta \cos^2\theta $$.

Calculate the value of $$\sqrt {\dfrac {9\sin^{2} \theta + 9\cos^{2} \theta}{4}} $$.