Introduction to...

$$\displaystyle \frac{4}{3}\cot ^{2}30^{\circ}+3\sin ^{2}60^{\circ}-2\text{cosec} ^{2}60^{\circ}-\frac{3}{4}\tan ^{2}30^{\circ}$$ is 

$$\displaystyle \frac{4}{\cot ^{2}30^{\circ}}+\frac{1}{\sin^{2}60^{\circ} }-\cos ^{2}45^{\circ}$$ is

If $$\displaystyle \tan 32^0.\cot (90^0-\theta )=1$$ find $$\theta $$.

The value of the expression $$\displaystyle \frac{5\sin ^{2}30^{\circ}+\cos ^{2}45^{\circ}+4\tan ^{2}60^{\circ}}{2\sin 30^{\circ}\cos 60^{\circ}+\tan 45^{\circ}}$$ is 

The value of $$\displaystyle \csc (65^0+\theta )-\sec (25^0-\theta )-\tan (55^0-\theta )+\cot (35^0+\theta )$$ is

Find the value of 
$$\displaystyle 4\left( { \sin }^{ 4 }{ 30 }^{ o }+{ \cos }^{ 4 }{ 60 }^{ o } \right) -3\left( { \sin }^{ 2 }{ 45 }^{ o }-2{ \cos }^{ 2 }{ 45 }^{ o } \right) $$

The value of $$\displaystyle \frac{2\sin 67^{\circ}}{\cos 23^{\circ}}-\frac{\cot 40^{\circ}}{\tan 50^{\circ}}$$

The value of $$tan\;1^{\circ}\;tan\;2^{\circ}\;tan\;3^{\circ}....tan\;89^{\circ}$$ is

The value of  $$\displaystyle { \text{cosec} }^{ 2 }\left( { 90 }^{ o }-\theta  \right) -{ \tan }^{ 2 }\theta $$ is :

$$\displaystyle \tan { { 5 }^{ o } } .\tan { { 40 }^{ o } } .\tan { 4{ 5 }^{ o } } .\tan { { 50 }^{ o } } .\tan { 8{ 5 }^{ o } } $$ is equal to :